Research ArticleGoodwill and System Dynamics Modeling for Film InvestmentDecision by Interactive Efforts

Jian Feng and Bin Liu

School of Economics and Management Shanghai Maritime University Shanghai 201306 China

Correspondence should be addressed to Bin Liu liubinshmtueducn

Received 8 May 2018 Accepted 26 August 2018 Published 13 September 2018

Academic Editor Lu Zhen

Copyright copy 2018 Jian Feng andBin LiuThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Academic research pertaining to the marketing of film industry has identified advertising film-making and star power as theimportant factors influencing a moviersquos market performance Prior research however has not investigated the joint influences ofthese factors The current study has extended previous research by analyzing the investment decision of studios or investors Inorder to analyze the optimal film investment decision in advertising film-making and stars power this paper develops a goodwillmodel and system dynamic (SD) model which allow us to disentangle the effects of advertising film-making and star power onfilm market performance The results show that the film producer should increasingly lay emphasis on investing in advertisingto absorb moviegoersrsquo attention Then the film producer should focus on investing in film-making when film quality has a greatimpact on the movies reputation and audiences viewing decision Furthermore the film producer should pay more attention tothe higher cost-performance stars who have more reasonable remuneration better acting skills and bigger box-office guaranteeMoreover the numerical analysis reveals that rational audience contributemore than fans to amovies box-office and bankable starscontribute more than high-profile stars to a movies returns Through SD simulation analysis the film series yields higher profitsthan new theme movies although the cost of investment is the same

1 Introduction

In the film industry the investors are expected to make thebest decisions involved in lots of funds in the shortest possibletime [1] According to Schwartz [2] ldquoIndustry estimatesreveal that 60 percent or more of movies produced each yearare box-office flops those that do resonate with viewers cangenerate a pretty penny for investorsrdquo There are some caseswhere promising movies show poor box-office performanceand inconspicuous movies show unexpectedly good results[3] ldquoMake no mistakerdquo shows that investing in films is arisky business [4ndash8] If investment decisions fail the costs ofthese mistakes for consumers are only the ticket price and anopportunity cost but the costs for investors or producers arehighly expensive [9] Success (or mere survivability) largelydepends on quickly aligning the organizational resourceslike genre director super stars advertising technical effectsrelease time etc [1 10] The main factors affecting thefinancial success of a movie are of great use in making invest-ment decisions The film industry uses different hallmarks

of quality in an attempt to control the level of uncertaintyWewill categorize the factors contributing to film investmentobserved in the documents into three main effects theadvertising effect film-making effect and the star powereffect

The advertising effect refers to the fact that studios pro-mote their ownmovies to increase the number of moviegoersand the box-office revenues through advertising channelssuch as the release conference the titbits the trailers andshow tours Nowadays there are multiple channels bothonline and offline for advertising delivery Typical examplesare Weibo (microblog) WeChat variety show and outdoorbillboard [11] Frequent new product introductions and rapidturnover lead movie studios to advertise heavily Movieadvertising is an effective measure to influence consumersrsquoquality perception [12] It has been confirmed by previousscholars that advertising plays a crucial role in a moviersquossuccess [13ndash15] During the moviersquos prerelease period adver-tising would inform viewers of the movies characteristicsand signal potential studio profit ability to investors What is

HindawiDiscrete Dynamics in Nature and SocietyVolume 2018 Article ID 7521689 10 pageshttpsdoiorg10115520187521689

2 Discrete Dynamics in Nature and Society

more effective movie advertising can not only lead to success(or failure) of a single movie at the box-office but also resultin an increase (or decrease) of the releasing studiorsquos marketvalue [16] Therefore advertising effect is the first importantfactor contributing to film investment

The film-making effect refers to factors including aninitial story or idea through screenwriting casting shootingsound recording and reproduction editing and screeningthe finished product before a movie showing A quan-titative approach using a combination of screenwritingdomain knowledge natural-language processing techniquesand modern statistical learning methods will help studiosevaluate scripts and improve a moviersquos gross return oninvestment [17 18] Compared with advertising and starpower the film-making gives more direct impact on amoviersquosword-of-mouth in the eyes of the audience For examplethe top three moviesmdashStar Wars ET the Extra-Terrestrialand Titanicmdashhad no stars but it is the movie itselfmdashnotthe starmdashthat makes the success [19] The word-of-mouthknown as the passing of information from person to personis a method used by consumers to express their experiencesand feelings about a brand product or service withoutintending to take part inmarketing and promotion [20] Sincemovie is a kind of good experience potential consumers mayhave difficulty in evaluating film-making quality and usuallysearch for former consumer opinions In this paper theword-of-mouth refers to the moviegoerrsquos reviews and movie ratingson the level of film-making [21ndash23] Industry experts agreethat word-of-mouth is a critical factor underlying a moviersquosstaying power which remains a powerful source for movieconsumers and leads to its ultimate financial success [1424] Duan et al also found that both a moviersquos box-officerevenue and word-of-mouth valence significantly influenceword-of-mouth volume Word-of-mouth volume in turnleads to higher box-office performance [25 26] Additionallywe often observe that some movies produced within muchsmaller budgets have achieved great success by utilizing viralmarketing through word-of-mouth (egTheHangoverWolfWarriors II) Consequently film-making effect is the secondvital factor involved with film investment The experience ofa producer is a considerable factor which is as powerful asdirector and actor [27]

The star (eg award winning actor and director) powereffect on film success has yielded somewhat mixed resultsSome papers have reported a positive relationship betweenthe presence of a star and box-office revenues [28 29] How-ever another scholars found no relationship even negativeeffects between stars and theatrical revenues [30ndash34] Even inthe study of star power the director and actor have differentdegrees of importance to a movie success Most studies haveindicated that director power is not very significant and attimes is much weaker than an actor power [3 35] Howeverin China a director plays a bigger role than actor regardingthe box-office [36] Meanwhile the high-profile stars are ableto command high fees which itself contributed to the highbudgets of their films often disproportionately so [32] Thatis to say high-profile stars are not always equal to methodactors Last but not least the star (actor and director) powereffect is the third crucial factor in regard to film investment

There is very little literature which focus on above factorsrsquoimpact on financial performance of the film from the per-spective of investment decisions Both the filmrsquos reputationand box-office success are not solely influenced by individualmovie attributes such as advertising production directoractor distributor release season and screen number whichalso depended on the causal relationship among all attributesrelated to movies [3] Our paper departs from the recentliterature and focuses on joint influences of these interactivefactors not just one single factor Interestingly this paperconsiders the investment decision of studios or investors anddevelops a goodwill model and system dynamic (SD) modelwhich allow us to disentangle the comprehensive effects ofadvertising film-making and star power

The rest of the paper is organized as follows In Section 2we will present an expanded Nerlove-Arrow model demandfunction and profit functions by using differential game InSection 3 based on the expanded Nerlove-Arrow model wewill derive the game equilibrium solution of film investorsand introduce four star selection strategies Then accordingto the four star selection scenarios we will discuss the cost-benefit of film investment by taking spectator heterogeneityand film heterogeneity into account separately In Section 4we will develop a SD model of film goodwill to reflect thedynamic impact of advertising film-making and star poweron moviegoers and box-office then we will simulate box-office trend in the filmrsquos release cycle Concluding remarksand managerial implications are discussed in the last section

2 Model Development and Notations

A movie is considered in this paper The film producersmake investment decisions in order to attract the majorityof moviegoers who focus on the advertising film-makingand star power in a movie We introduce the notations in thispaper as shown in Table 1

We assume that the change of film goodwill follows theNerlove-Arrow framework [37 38] ie

∙119866 (119905) = 120572119860 (119905) + 120573119872(119905) + 120578119878 (119905) minus 120575119866 (119905) (1)

We suppose that advertising and star power have directeffects on the number of moviegoers The film-making effortindirectly influences moviegoers through word-of-mouththat is filmrsquos goodwillThe number ofmoviegoers satisfies thefollowing equation

119873(119905) = 120590119878 + 120574119860 + 120576119866 (2)

Similar to the previous literature such as Feng andLiu [38] the advertising cost film-making cost and starremuneration functions are quadratic with marketing effortsrespectively namely 119862(119860) = (1205831198602)1198602(119905) 119862(119872) =(1205831198722)1198722(119905) and 119862(119878) = (1205831198782)1198782(119905)

Furthermore we assume that the filmrsquos investment fundsare not constrained and have a common positive discountrate 120582 For the convenience of calculation we suppose thatthe distribution cost of the film is zero The film producers

Discrete Dynamics in Nature and Society 3

Table 1 Variables and definitions used in the model

119905 Time 119905 119905 ge 0119866 (119905) The accumulated filmrsquos goodwill at time t119860(119905) The filmrsquos advertising effort at time t119872(119905) The film-making effort at time t119878(119905) The star power at time t119873(119905) The number of moviegoers along time t119862(119860) The filmrsquos advertising cost119862(119872) The film-making cost119862(119878) The star remuneration120583119860 120583119872120583119878

Constants119901 The film ticket price119869 The objective profit functions of the film120572gt0 Positive coefficient measuring the impact of filmrsquos advertising120573gt0 Positive coefficient measuring the impact of film-making120578gt0 Positive coefficient measuring the impact of star power120575gt0 The decay rate of the film goodwill120590gt0 Positive constant representing the effect of star power on the number of moviegoers120574gt0 Positive constant representing the effect of filmrsquos advertising on the number of moviegoers120576gt0 Positive constant representing the effect of filmrsquos goodwill on the number of moviegoers120582gt0 The discount rate

and investors strive to maximize their profit Then the filmrsquosobjective function is

119869 = intinfin0

119890minus120582119905 [119901 times 119873 (119905) minus 1205831198602 1198602 (119905) minus 1205831198722 1198722 (119905)minus 1205831198782 1198782 (119905)] 119889119905

(3)

3 Equilibrium Solutions andNumerical Analysis

31 Equilibrium Solutions

Proposition 1 Film investorsrsquo equilibrium strategies are givenas follows

(1) The film advertising effort is

119860lowast = 120576120572119901(120575 + 120582) 120583119860 +

120574119901120583119860 (4)

(2) The film-making effort is

119872lowast = 120576120573119901(120575 + 120582) 120583119872 (5)

(3) The film star power effort is

119878lowast = 120576120578119901(120575 + 120582) 120583119878 +

120590119901120583119878 (6)

(4) The film investorrsquos profit under the equilibrium condi-tion is

119881lowast (119866) = 120576119901120575 + 120582119866 + 120576119901

120575 + 120582 [120572119901120583119860 +1205722120576119901

(120575 + 120582) 120583119860+ 1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878 +1205782120576119901

(120575 + 120582) 120583119878] minus 1205831198782 [120590119901120583119878+ 120578120576119901(120575 + 120582) 120583119878 ]

2 + 119901[120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860 +120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [ 120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872

(7)

Proof See the Appendix

Proposition 1 illustrates the following insights (i) Thefilm producer increasingly lays emphasis on investing in filmadvertising such as releasing conference titbits trailers andshow tours so as to absorb moviegoersrsquo attention Due toProposition 1 there are three positive correlations as followsOne is the relationship between investment in film advertis-ing and advertising contribution to film goodwill The otheris the relationship between investment in film advertisingand advertising contribution to the number of moviegoersThe last one is the relationship between investment in filmadvertising and film goodwillrsquos contribution to the numberof moviegoers (ii) The investment in film-making has pos-itive correlation with both film-making contribution to film

4 Discrete Dynamics in Nature and Society

Table 2 Movie star selection strategies

Box-office guarantee No box-office guaranteeHigh movie remuneration Strategy 1 (H G) Strategy 2 (H NG)Low movie remuneration Strategy 3 (L G) Strategy 4 (L NG)

Table 3 Parameters assignment of rational audiences

120572 120573 120578 120590 120574 120576

Strategy 1 (H G) 01 05 04 05 01 04Strategy 2 (H NG) 01 05 01 01 01 04Strategy 3 (L G) 01 05 04 05 01 04Strategy 4 (L NG) 01 05 01 01 01 04

Table 4 Parameters assignment of fans

120572 120573 120578 120590 120574 120576

Strategy 1 (H G) 01 02 07 07 01 02Strategy 2 (H NG) 01 02 07 01 01 02Strategy 3 (L G) 01 02 07 07 01 02Strategy 4 (L NG) 01 02 01 01 01 02

goodwill and its impact on audiencersquos viewing decision Themore attention that film producer pays to investing in film-making the more importance moviegoers attach to the filmrsquosquality On the contrary the film producer will reduce film-making investment if the audience pursue actor or directorin a movie So there are lots of shoddy movies which focuson the star popularity but ignore film-making quality (iii)The investment in star has positive correlation with both starcontribution to film goodwill and its impact on audiencersquosviewing decision When the star popularity hugely influencesfilm goodwill and potential audiences the film investorswould like to invite well-known directors or famous actorswhose cost performance is higher to participate in a movie

32 Numerical Analysis and Strategic Comparative Analysis

321 Star Selection and Spectator Heterogeneity

(1) Star SelectionThe star selection as a critical component ofthe film investment has a huge influence on the outcome ofbox-office which has been largely ignored in past academicresearch [39] The selection of movie stars by film investorcan be divided into four strategies (in Table 2) according tothe remuneration and box-office guarantee The higher theremuneration thatmovie stars earn the larger the120583119878 and viceversa The value of 120572 and 120574 is large if movie stars can bringhigh box-office and vice versa

(2) Spectator Heterogeneity Anecdotal evidence suggests thatthe presence of superstars is not always a guarantee of successand hence a deeper study is required to analyze the potentialaudience of a movie [7] Therefore this paper considersthe film audience to be heterogeneous We only considerspectator heterogeneity rational audiences and fans Theformerrsquos proportion is 120596 and the latterrsquos share is 1-120596

It is also assumed that the film ticket price is constant p=1Let 120583119860 = 120583119872 = 1 120582=120575=005 We assume that advertising hasweak influence on film goodwill andmoviegoers so the rangeof 120572 and 120574 is small

(1) Rational audiences They lay more attention on film-making and film goodwill Therefore 120573 and 120576 have highervalues see Table 3

(2) Fans They lay emphasis on famous actor or directorTherefore 120578 has a higher value but 120573 and 120576 have lower valuessee Table 4

(3) Investment Analysis of Spectator Heterogeneity On thebasis of equilibrium solutions and numerical values we drawbar charts shown in Figure 1 The films investment strategyvaries as the rational audience and fans have different viewingrequirements for the film Studios give high investmentin film-making in the face of rational audiences But theinvestment in star is high in order to cater to the fansFirstly the studiosrsquo investment in film advertising is thesame whether for the rational audiences or fans Secondlybecause the film-making level has a great impact on word-of-mouth studios increase investment in film-making toingratiate rational audiences but economize the film-makingcosts in the face of fans Thirdly among these 4 strategies ofstar selection the film investment in strategy 3 is the highestand significantly higher than the sum of investments inadvertising and film-makingMeanwhile the film investmentin strategy 3 is several times higher than the cost of actorsin other strategies The investment in star of strategy 1 is thesecond and strategy 2 gives lowest investment in star whenfacing with the rational audiences But for fans strategy 4has the second investment to star and strategy 2 gives lowestinvestment in star No matter rational audiences or fans thestar selection in strategy 3 is the most cost-effective while thestar cost-effectiveness of strategy 2 is minimum

Discrete Dynamics in Nature and Society 5

0010203040506070809

advertising filmmaking star

Rational audiences

0

05

1

15

2

25

advertising filmmaking star

Fans

Strategy 1Strategy 2

Strategy 3Strategy 4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 1 Investment analysis of spectator heterogeneity

In fact above analysis is precisely the case of invest-ment made by film producers For example when selectingactors and actresses film producers comprehensively take thecombination of male and female protagonists into accountIn Hong Kong movies for instance ldquoaward winning actorsfrom Hong Kong usually work together with Chinese main-land second-tier actressesrdquo or ldquoChinese mainland first-tireactresses usually work together with second and third-tieractors from Hong Kong and Taiwanrdquo While consideringthe number of fans they would arrange some well-knownsecond- and third-tier stars with reasonable remuneration

322 FilmHeterogeneity and Numerical Analysis This paperdivides the film genre into new theme film and film series(eg Star Trek Pirates of the Caribbean or Fast amp Furious)Compared with new theme films films series refer to contin-uous multiset serial movies The numerical analysis of filminvestment performance is as follows

(1) New Theme Film (1) Cost analysis The movie cost underdifferent star selection strategies is shown in Figure 2 (thevertical axis is dimensionless) The investment cost underdifferent strategies increases with the proportion of rationalaudience (120596 is the proportion of rational audience 120596 isin[0 1]) The cost increment of strategy 3 is the highest andthat of strategy 4 is the lowest On the one hand the costof strategies 3 and 4 is higher than that of strategies 1 and 2when fans are the main spectator group On the other handwhen rational audience accounts for a large proportion thetotal cost of strategy 1 is higher than that of strategy 4 but thecost of strategy 2 and strategy 4 tends to approach each otherOverall the investment cost of strategy 3 is the highest andthat of strategy 2 is the lowest Nomatter what kind ofmoviesthe investment cost of rational audience is higher than that offans

(2) The number of moviegoers and the box-office analysisFigure 3 (the vertical axis is dimensionless) shows that high-paid stars contribute less to the number of moviegoers thanthe low-paid ones The reason is that over-high cost limitsfilm producersrsquo investment in high-profile stars Although thehigh popularity of stars makes a huge contribution to thenumber of moviegoers the over-high remuneration lowersstars cost performance At the same time the higher cost

02 04 06 08 10

1

2

3

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 2 Total movie cost under different star selection strategies

02 04 06 08 10

4

6

8

10

Strategy 1Strategy 2

Strategy 3Strategy 4

2

Figure 3 Moviegoers of new theme film under different starselection strategies

performance makes producers increase the star investmentand also increase the number of moviegoers Bankable starstruly guarantee the box-office and the influence of such starson the number of moviegoers is great As the proportion ofrational audience increases this influence is more significantIt can be interpreted that rational audience always pay moreattention to actors acting skills and film-making quality And

6 Discrete Dynamics in Nature and Society

box-office guarantee means getting the audiencersquos approvalin the aspects of directors acting skills script selection etcThe audience loyalty to bankable stars is higher and then thenumber of moviegoers is more

In Figure 3 the biggest number of moviegoers is instrategy 3 which has the participation of the low-paid butbankable stars so-called low-profile stars with real strengthThese stars own good acting skills loyal audience relativelyreasonable remuneration and high cost performance There-fore strategy 3 has a relatively strong influence on both fansand the rational audience and earns more expected profitsthan other strategies The smallest number of moviegoersis in strategy 2 which has the participation of the high-paid but with no box-office guaranteed actors Despite suchstars having high popularity their acting skills have beenquestioned and criticized by moviegoers Generally themovie they are involved in has no guarantee at the box-officeand its online word-of-mouth is also poor

It is generally recognized that fans are an importantcriterion for film producers to choose actors But Figure 5shows that rational audiences are the main guarantee of box-office rather than fans Due to that film producers investmentin rational audiences is higher than that in fans the marketperformance of rational audiences is better than that of fansThe number of moviegoers is directly proportional to theratio of rational audience and is inversely proportional to theratio of fans So it is easy to understand the poor box-officeperformance of movies starring high-paid ldquolittle fresh meatrdquowho have a huge number of fans but no box-office guaranteeFor actors who have no box-office guarantee as the numberof fans decreases moviegoers in strategy 2 with high-paidactors will outnumber strategy 4 with low-paid actors whichis mainly because of the impact of star popularity on themovies reputation

Meanwhile with the development of network film pro-ducers paymore andmore attention tomoviegoersrsquo opinionsFor example during the preparation of many movies as aresult of fansrsquo doubts and dissatisfaction with the star lineupthe incident of changing actors occurs frequently This alsoshows film producersrsquo expectations for moviegoers and box-office and their consideration about starsrsquo impact on filmreputation when making investment decisions At the sametime with the changes of online word-of-mouth after themovie is released the reputation of stars changes accordinglySome stars may surge in popularity because of their excellentacting skills which further enhances the reputation of themovie some actors are questioned because of poor actingskills resulting in damage to the movie reputation and box-office slump

(3) Revenue analysis The final revenue of a movie isaffected by box-office and investment costs This paperfocuses on film investment decision-making and the ulti-mate goal is tomaximize themoviersquos revenueWe assume thatthe revenues of all strategies are positive and the vertical axisis dimensionless Figure 4 shows that the higher the rationalaudience ratio the higher the movie revenue Because whenthe film investor expects a movie to be positive and supposesthat the rational audience is influenced by the word-of-mouth with the increase of moviegoers the accumulation

02 04 06 08 10

2

3

5

6

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 4 Revenue of new theme film under different strategies

02 04 06 08 10

4

6

8

10

2

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 5 Moviegoers of film series under different star selectionstrategies

of online word-of-mouth will increase the possibility ofaudiencersquos going to cinema thus increasing the film revenueIt is easy to understand that corresponding to the numberof moviegoers revenues of movies played by bankable starsare higher than that with no box-office guaranteed stars Inaddition under costrsquos influence revenues of movies playedby low-paid actors are higher than that of high-paid actors

(2) Film Series Film series have a high reputation in the earlystage of film release due to the accumulation of early seriesHigh film reputation does not change the investment strategyso the investment cost of film series is consistent with that ofa new thememovie As shown in Figures 5 and 6 (the verticalaxis is dimensionless) influenced by accumulated popularitythe number of film seriesrsquo moviegoers and its revenues arehigher than that of a new theme movie That is why filmproducers prefer giving investment in sequel movies ratherthan new theme movies when there is a good response to theserialmoviesTherefore there are alwaysmovies based onTVdramas variety shows and popular online novels Besides itis also easy to understand that the same story (eg Journeyto the West) is reshot over and over again All the above are

Discrete Dynamics in Nature and Society 7

02 04 06 08 10

2

3

5

6

4

7

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 6 Revenue of film series under different star selectionstrategies

the cases in which film producers take advantage of the highreputation accumulated before

Similarly the audience keeping high loyalty to some actoror director (being a fan of the star or director) on the onehand is the recognition of the directors directing skills oractors acting skills and on the other hand the director oractors reputation that accumulated over a long period oftime gives them a box-office guarantee in the mind of spec-tator Therefore the relationship between actors directorsand movies should be mutual promotion when an actorspopularity and acting skills or directors directing ability havehigh-performance in online word-of-mouth and box-officethen the movie will further enhance and consolidate theactors or the directors popularity

4 System Dynamics Analysis of Film Goodwilland Box-Office

41 The System Dynamics Model System dynamics is awell-established methodology to model and understand thebehavior of complex systems and it has been extensively usedfor modeling the dynamic behavior of complex nonlinearsystems [40 41] Based on the above filmrsquos goodwill modelthe SD model of film goodwill reflects the dynamic impactof advertising film-making and star power on film perfor-mance The advertising and star power factors have directeffects on the box-office and the film-making effort indirectlyinfluences the box-office through film goodwill Then thebox-office in turn affects the three factors Figure 7 shows thestock and flowdiagram for the systemdynamicsmodel of filmgoodwill by SD software-Vensim version 71

42 The System Dynamics Analysis According to Chen andYin [42] movies have relatively short life cycles and theaverage exposure time of a movie is approximately onemonth Based on SD model in Section 41 and equilibriumsolutions in Section 3 we will analyze four star selectionstrategies of new theme film by SD simulation Then we getthe box-office trend of rational audiences and fans duringthe release period as shown in Figures 8 and 9 (the vertical

axis of box-office is dimensionless) In Figures 3 and 8 forrational moviegoers strategy 3 has a higher investment instars who are reasonably paid with box-office guarantee andthe film-making is excellent Compared with other moviesstrategy 3 can have a good performance at the early stageof release time and the potential development is great Asa result it has considerable returns on investment Movies(Strategies 1 2 and 4) are ordinary in performance Exceptfor movies (Strategy 1) played by high-paid bankable starswhose performance is slightly better the box-office of othermovies (Strategies 2 and 4) is close In Figures 2 and 9 forfans even though their idols act in the movies they do notpay much for the low-quality film-making Particularly instrategies 1 and 2 due to bad word-of-mouth caused by lowinvestment in film-making movies with high popularity starscannot achieve good performance if just relying on fans effectFor movies with high investment in film-making obviouslybankable stars are far more attractive to audience than thatwith no box-office guarantee But generally the performanceof movies with high investment in film-making is better thanthat with low investment in film-making

In summary in order to maximize the profit fromProposition 1 film producers choose different types of starsaccording to different needs of moviegoers and thus makedifferent investment decisions However returns of filminvestment follow the principle that high investment getshigh returns Among film investment strategies strategy 3has the highest investment most moviegoers and highestreturns while strategy 2 has the lowest investment leastmoviegoers and least returns

Compared with new theme film what film series reflectin the SD simulation is nothing but the fact that initial valueof simulated box-office is higher Other performances of filmseries in the release period are consistent with new themefilm So the SD analysis of film series is omitted in this paperBecause of the accumulated high reputation the box-office offilm series is always better than that of new theme film

5 Concluding Remarks andManagerial Implications

This paper considers the joint effects of advertising film-making and star power on film reputation the numberof moviegoers and box-office We consider the investmentdecision of a movie made by studios or investors and developa goodwill model and system dynamic model which allowus to disentangle advertising film-making and star powereffects The results are proved as follows

Firstly the film producersrsquo investment in advertisingfilm-making and star power are positively correlated withtheir contribution to film reputation and the number ofmoviegoers but negatively correlatedwith the cost coefficientof three factors The film producer will increasingly layemphasis on investing in advertising such as the release con-ference titbits trailers and show tours to absorbmoviegoersrsquoattention The film producer focuses on investing in film-making when film quality has a great impact on the moviesreputation and the audiences viewing decision For invest-ment in stars the film producer paysmore attention to higher

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

Discrete Dynamics in Nature and Society 3

Table 1 Variables and definitions used in the model

119905 Time 119905 119905 ge 0119866 (119905) The accumulated filmrsquos goodwill at time t119860(119905) The filmrsquos advertising effort at time t119872(119905) The film-making effort at time t119878(119905) The star power at time t119873(119905) The number of moviegoers along time t119862(119860) The filmrsquos advertising cost119862(119872) The film-making cost119862(119878) The star remuneration120583119860 120583119872120583119878

Constants119901 The film ticket price119869 The objective profit functions of the film120572gt0 Positive coefficient measuring the impact of filmrsquos advertising120573gt0 Positive coefficient measuring the impact of film-making120578gt0 Positive coefficient measuring the impact of star power120575gt0 The decay rate of the film goodwill120590gt0 Positive constant representing the effect of star power on the number of moviegoers120574gt0 Positive constant representing the effect of filmrsquos advertising on the number of moviegoers120576gt0 Positive constant representing the effect of filmrsquos goodwill on the number of moviegoers120582gt0 The discount rate

and investors strive to maximize their profit Then the filmrsquosobjective function is

119869 = intinfin0

119890minus120582119905 [119901 times 119873 (119905) minus 1205831198602 1198602 (119905) minus 1205831198722 1198722 (119905)minus 1205831198782 1198782 (119905)] 119889119905

(3)

3 Equilibrium Solutions andNumerical Analysis

31 Equilibrium Solutions

Proposition 1 Film investorsrsquo equilibrium strategies are givenas follows

(1) The film advertising effort is

119860lowast = 120576120572119901(120575 + 120582) 120583119860 +

120574119901120583119860 (4)

(2) The film-making effort is

119872lowast = 120576120573119901(120575 + 120582) 120583119872 (5)

(3) The film star power effort is

119878lowast = 120576120578119901(120575 + 120582) 120583119878 +

120590119901120583119878 (6)

(4) The film investorrsquos profit under the equilibrium condi-tion is

119881lowast (119866) = 120576119901120575 + 120582119866 + 120576119901

120575 + 120582 [120572119901120583119860 +1205722120576119901

(120575 + 120582) 120583119860+ 1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878 +1205782120576119901

(120575 + 120582) 120583119878] minus 1205831198782 [120590119901120583119878+ 120578120576119901(120575 + 120582) 120583119878 ]

2 + 119901[120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860 +120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [ 120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872

(7)

Proof See the Appendix

Proposition 1 illustrates the following insights (i) Thefilm producer increasingly lays emphasis on investing in filmadvertising such as releasing conference titbits trailers andshow tours so as to absorb moviegoersrsquo attention Due toProposition 1 there are three positive correlations as followsOne is the relationship between investment in film advertis-ing and advertising contribution to film goodwill The otheris the relationship between investment in film advertisingand advertising contribution to the number of moviegoersThe last one is the relationship between investment in filmadvertising and film goodwillrsquos contribution to the numberof moviegoers (ii) The investment in film-making has pos-itive correlation with both film-making contribution to film

4 Discrete Dynamics in Nature and Society

Table 2 Movie star selection strategies

Box-office guarantee No box-office guaranteeHigh movie remuneration Strategy 1 (H G) Strategy 2 (H NG)Low movie remuneration Strategy 3 (L G) Strategy 4 (L NG)

Table 3 Parameters assignment of rational audiences

120572 120573 120578 120590 120574 120576

Strategy 1 (H G) 01 05 04 05 01 04Strategy 2 (H NG) 01 05 01 01 01 04Strategy 3 (L G) 01 05 04 05 01 04Strategy 4 (L NG) 01 05 01 01 01 04

Table 4 Parameters assignment of fans

120572 120573 120578 120590 120574 120576

Strategy 1 (H G) 01 02 07 07 01 02Strategy 2 (H NG) 01 02 07 01 01 02Strategy 3 (L G) 01 02 07 07 01 02Strategy 4 (L NG) 01 02 01 01 01 02

goodwill and its impact on audiencersquos viewing decision Themore attention that film producer pays to investing in film-making the more importance moviegoers attach to the filmrsquosquality On the contrary the film producer will reduce film-making investment if the audience pursue actor or directorin a movie So there are lots of shoddy movies which focuson the star popularity but ignore film-making quality (iii)The investment in star has positive correlation with both starcontribution to film goodwill and its impact on audiencersquosviewing decision When the star popularity hugely influencesfilm goodwill and potential audiences the film investorswould like to invite well-known directors or famous actorswhose cost performance is higher to participate in a movie

32 Numerical Analysis and Strategic Comparative Analysis

321 Star Selection and Spectator Heterogeneity

(1) Star SelectionThe star selection as a critical component ofthe film investment has a huge influence on the outcome ofbox-office which has been largely ignored in past academicresearch [39] The selection of movie stars by film investorcan be divided into four strategies (in Table 2) according tothe remuneration and box-office guarantee The higher theremuneration thatmovie stars earn the larger the120583119878 and viceversa The value of 120572 and 120574 is large if movie stars can bringhigh box-office and vice versa

(2) Spectator Heterogeneity Anecdotal evidence suggests thatthe presence of superstars is not always a guarantee of successand hence a deeper study is required to analyze the potentialaudience of a movie [7] Therefore this paper considersthe film audience to be heterogeneous We only considerspectator heterogeneity rational audiences and fans Theformerrsquos proportion is 120596 and the latterrsquos share is 1-120596

It is also assumed that the film ticket price is constant p=1Let 120583119860 = 120583119872 = 1 120582=120575=005 We assume that advertising hasweak influence on film goodwill andmoviegoers so the rangeof 120572 and 120574 is small

(1) Rational audiences They lay more attention on film-making and film goodwill Therefore 120573 and 120576 have highervalues see Table 3

(2) Fans They lay emphasis on famous actor or directorTherefore 120578 has a higher value but 120573 and 120576 have lower valuessee Table 4

(3) Investment Analysis of Spectator Heterogeneity On thebasis of equilibrium solutions and numerical values we drawbar charts shown in Figure 1 The films investment strategyvaries as the rational audience and fans have different viewingrequirements for the film Studios give high investmentin film-making in the face of rational audiences But theinvestment in star is high in order to cater to the fansFirstly the studiosrsquo investment in film advertising is thesame whether for the rational audiences or fans Secondlybecause the film-making level has a great impact on word-of-mouth studios increase investment in film-making toingratiate rational audiences but economize the film-makingcosts in the face of fans Thirdly among these 4 strategies ofstar selection the film investment in strategy 3 is the highestand significantly higher than the sum of investments inadvertising and film-makingMeanwhile the film investmentin strategy 3 is several times higher than the cost of actorsin other strategies The investment in star of strategy 1 is thesecond and strategy 2 gives lowest investment in star whenfacing with the rational audiences But for fans strategy 4has the second investment to star and strategy 2 gives lowestinvestment in star No matter rational audiences or fans thestar selection in strategy 3 is the most cost-effective while thestar cost-effectiveness of strategy 2 is minimum

Discrete Dynamics in Nature and Society 5

0010203040506070809

advertising filmmaking star

Rational audiences

0

05

1

15

2

25

advertising filmmaking star

Fans

Strategy 1Strategy 2

Strategy 3Strategy 4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 1 Investment analysis of spectator heterogeneity

In fact above analysis is precisely the case of invest-ment made by film producers For example when selectingactors and actresses film producers comprehensively take thecombination of male and female protagonists into accountIn Hong Kong movies for instance ldquoaward winning actorsfrom Hong Kong usually work together with Chinese main-land second-tier actressesrdquo or ldquoChinese mainland first-tireactresses usually work together with second and third-tieractors from Hong Kong and Taiwanrdquo While consideringthe number of fans they would arrange some well-knownsecond- and third-tier stars with reasonable remuneration

322 FilmHeterogeneity and Numerical Analysis This paperdivides the film genre into new theme film and film series(eg Star Trek Pirates of the Caribbean or Fast amp Furious)Compared with new theme films films series refer to contin-uous multiset serial movies The numerical analysis of filminvestment performance is as follows

(1) New Theme Film (1) Cost analysis The movie cost underdifferent star selection strategies is shown in Figure 2 (thevertical axis is dimensionless) The investment cost underdifferent strategies increases with the proportion of rationalaudience (120596 is the proportion of rational audience 120596 isin[0 1]) The cost increment of strategy 3 is the highest andthat of strategy 4 is the lowest On the one hand the costof strategies 3 and 4 is higher than that of strategies 1 and 2when fans are the main spectator group On the other handwhen rational audience accounts for a large proportion thetotal cost of strategy 1 is higher than that of strategy 4 but thecost of strategy 2 and strategy 4 tends to approach each otherOverall the investment cost of strategy 3 is the highest andthat of strategy 2 is the lowest Nomatter what kind ofmoviesthe investment cost of rational audience is higher than that offans

(2) The number of moviegoers and the box-office analysisFigure 3 (the vertical axis is dimensionless) shows that high-paid stars contribute less to the number of moviegoers thanthe low-paid ones The reason is that over-high cost limitsfilm producersrsquo investment in high-profile stars Although thehigh popularity of stars makes a huge contribution to thenumber of moviegoers the over-high remuneration lowersstars cost performance At the same time the higher cost

02 04 06 08 10

1

2

3

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 2 Total movie cost under different star selection strategies

02 04 06 08 10

4

6

8

10

Strategy 1Strategy 2

Strategy 3Strategy 4

2

Figure 3 Moviegoers of new theme film under different starselection strategies

performance makes producers increase the star investmentand also increase the number of moviegoers Bankable starstruly guarantee the box-office and the influence of such starson the number of moviegoers is great As the proportion ofrational audience increases this influence is more significantIt can be interpreted that rational audience always pay moreattention to actors acting skills and film-making quality And

6 Discrete Dynamics in Nature and Society

box-office guarantee means getting the audiencersquos approvalin the aspects of directors acting skills script selection etcThe audience loyalty to bankable stars is higher and then thenumber of moviegoers is more

In Figure 3 the biggest number of moviegoers is instrategy 3 which has the participation of the low-paid butbankable stars so-called low-profile stars with real strengthThese stars own good acting skills loyal audience relativelyreasonable remuneration and high cost performance There-fore strategy 3 has a relatively strong influence on both fansand the rational audience and earns more expected profitsthan other strategies The smallest number of moviegoersis in strategy 2 which has the participation of the high-paid but with no box-office guaranteed actors Despite suchstars having high popularity their acting skills have beenquestioned and criticized by moviegoers Generally themovie they are involved in has no guarantee at the box-officeand its online word-of-mouth is also poor

It is generally recognized that fans are an importantcriterion for film producers to choose actors But Figure 5shows that rational audiences are the main guarantee of box-office rather than fans Due to that film producers investmentin rational audiences is higher than that in fans the marketperformance of rational audiences is better than that of fansThe number of moviegoers is directly proportional to theratio of rational audience and is inversely proportional to theratio of fans So it is easy to understand the poor box-officeperformance of movies starring high-paid ldquolittle fresh meatrdquowho have a huge number of fans but no box-office guaranteeFor actors who have no box-office guarantee as the numberof fans decreases moviegoers in strategy 2 with high-paidactors will outnumber strategy 4 with low-paid actors whichis mainly because of the impact of star popularity on themovies reputation

Meanwhile with the development of network film pro-ducers paymore andmore attention tomoviegoersrsquo opinionsFor example during the preparation of many movies as aresult of fansrsquo doubts and dissatisfaction with the star lineupthe incident of changing actors occurs frequently This alsoshows film producersrsquo expectations for moviegoers and box-office and their consideration about starsrsquo impact on filmreputation when making investment decisions At the sametime with the changes of online word-of-mouth after themovie is released the reputation of stars changes accordinglySome stars may surge in popularity because of their excellentacting skills which further enhances the reputation of themovie some actors are questioned because of poor actingskills resulting in damage to the movie reputation and box-office slump

(3) Revenue analysis The final revenue of a movie isaffected by box-office and investment costs This paperfocuses on film investment decision-making and the ulti-mate goal is tomaximize themoviersquos revenueWe assume thatthe revenues of all strategies are positive and the vertical axisis dimensionless Figure 4 shows that the higher the rationalaudience ratio the higher the movie revenue Because whenthe film investor expects a movie to be positive and supposesthat the rational audience is influenced by the word-of-mouth with the increase of moviegoers the accumulation

02 04 06 08 10

2

3

5

6

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 4 Revenue of new theme film under different strategies

02 04 06 08 10

4

6

8

10

2

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 5 Moviegoers of film series under different star selectionstrategies

of online word-of-mouth will increase the possibility ofaudiencersquos going to cinema thus increasing the film revenueIt is easy to understand that corresponding to the numberof moviegoers revenues of movies played by bankable starsare higher than that with no box-office guaranteed stars Inaddition under costrsquos influence revenues of movies playedby low-paid actors are higher than that of high-paid actors

(2) Film Series Film series have a high reputation in the earlystage of film release due to the accumulation of early seriesHigh film reputation does not change the investment strategyso the investment cost of film series is consistent with that ofa new thememovie As shown in Figures 5 and 6 (the verticalaxis is dimensionless) influenced by accumulated popularitythe number of film seriesrsquo moviegoers and its revenues arehigher than that of a new theme movie That is why filmproducers prefer giving investment in sequel movies ratherthan new theme movies when there is a good response to theserialmoviesTherefore there are alwaysmovies based onTVdramas variety shows and popular online novels Besides itis also easy to understand that the same story (eg Journeyto the West) is reshot over and over again All the above are

Discrete Dynamics in Nature and Society 7

02 04 06 08 10

2

3

5

6

4

7

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 6 Revenue of film series under different star selectionstrategies

the cases in which film producers take advantage of the highreputation accumulated before

Similarly the audience keeping high loyalty to some actoror director (being a fan of the star or director) on the onehand is the recognition of the directors directing skills oractors acting skills and on the other hand the director oractors reputation that accumulated over a long period oftime gives them a box-office guarantee in the mind of spec-tator Therefore the relationship between actors directorsand movies should be mutual promotion when an actorspopularity and acting skills or directors directing ability havehigh-performance in online word-of-mouth and box-officethen the movie will further enhance and consolidate theactors or the directors popularity

4 System Dynamics Analysis of Film Goodwilland Box-Office

41 The System Dynamics Model System dynamics is awell-established methodology to model and understand thebehavior of complex systems and it has been extensively usedfor modeling the dynamic behavior of complex nonlinearsystems [40 41] Based on the above filmrsquos goodwill modelthe SD model of film goodwill reflects the dynamic impactof advertising film-making and star power on film perfor-mance The advertising and star power factors have directeffects on the box-office and the film-making effort indirectlyinfluences the box-office through film goodwill Then thebox-office in turn affects the three factors Figure 7 shows thestock and flowdiagram for the systemdynamicsmodel of filmgoodwill by SD software-Vensim version 71

42 The System Dynamics Analysis According to Chen andYin [42] movies have relatively short life cycles and theaverage exposure time of a movie is approximately onemonth Based on SD model in Section 41 and equilibriumsolutions in Section 3 we will analyze four star selectionstrategies of new theme film by SD simulation Then we getthe box-office trend of rational audiences and fans duringthe release period as shown in Figures 8 and 9 (the vertical

axis of box-office is dimensionless) In Figures 3 and 8 forrational moviegoers strategy 3 has a higher investment instars who are reasonably paid with box-office guarantee andthe film-making is excellent Compared with other moviesstrategy 3 can have a good performance at the early stageof release time and the potential development is great Asa result it has considerable returns on investment Movies(Strategies 1 2 and 4) are ordinary in performance Exceptfor movies (Strategy 1) played by high-paid bankable starswhose performance is slightly better the box-office of othermovies (Strategies 2 and 4) is close In Figures 2 and 9 forfans even though their idols act in the movies they do notpay much for the low-quality film-making Particularly instrategies 1 and 2 due to bad word-of-mouth caused by lowinvestment in film-making movies with high popularity starscannot achieve good performance if just relying on fans effectFor movies with high investment in film-making obviouslybankable stars are far more attractive to audience than thatwith no box-office guarantee But generally the performanceof movies with high investment in film-making is better thanthat with low investment in film-making

In summary in order to maximize the profit fromProposition 1 film producers choose different types of starsaccording to different needs of moviegoers and thus makedifferent investment decisions However returns of filminvestment follow the principle that high investment getshigh returns Among film investment strategies strategy 3has the highest investment most moviegoers and highestreturns while strategy 2 has the lowest investment leastmoviegoers and least returns

Compared with new theme film what film series reflectin the SD simulation is nothing but the fact that initial valueof simulated box-office is higher Other performances of filmseries in the release period are consistent with new themefilm So the SD analysis of film series is omitted in this paperBecause of the accumulated high reputation the box-office offilm series is always better than that of new theme film

5 Concluding Remarks andManagerial Implications

This paper considers the joint effects of advertising film-making and star power on film reputation the numberof moviegoers and box-office We consider the investmentdecision of a movie made by studios or investors and developa goodwill model and system dynamic model which allowus to disentangle advertising film-making and star powereffects The results are proved as follows

Firstly the film producersrsquo investment in advertisingfilm-making and star power are positively correlated withtheir contribution to film reputation and the number ofmoviegoers but negatively correlatedwith the cost coefficientof three factors The film producer will increasingly layemphasis on investing in advertising such as the release con-ference titbits trailers and show tours to absorbmoviegoersrsquoattention The film producer focuses on investing in film-making when film quality has a great impact on the moviesreputation and the audiences viewing decision For invest-ment in stars the film producer paysmore attention to higher

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

4 Discrete Dynamics in Nature and Society

Table 2 Movie star selection strategies

Box-office guarantee No box-office guaranteeHigh movie remuneration Strategy 1 (H G) Strategy 2 (H NG)Low movie remuneration Strategy 3 (L G) Strategy 4 (L NG)

Table 3 Parameters assignment of rational audiences

120572 120573 120578 120590 120574 120576

Strategy 1 (H G) 01 05 04 05 01 04Strategy 2 (H NG) 01 05 01 01 01 04Strategy 3 (L G) 01 05 04 05 01 04Strategy 4 (L NG) 01 05 01 01 01 04

Table 4 Parameters assignment of fans

120572 120573 120578 120590 120574 120576

Strategy 1 (H G) 01 02 07 07 01 02Strategy 2 (H NG) 01 02 07 01 01 02Strategy 3 (L G) 01 02 07 07 01 02Strategy 4 (L NG) 01 02 01 01 01 02

goodwill and its impact on audiencersquos viewing decision Themore attention that film producer pays to investing in film-making the more importance moviegoers attach to the filmrsquosquality On the contrary the film producer will reduce film-making investment if the audience pursue actor or directorin a movie So there are lots of shoddy movies which focuson the star popularity but ignore film-making quality (iii)The investment in star has positive correlation with both starcontribution to film goodwill and its impact on audiencersquosviewing decision When the star popularity hugely influencesfilm goodwill and potential audiences the film investorswould like to invite well-known directors or famous actorswhose cost performance is higher to participate in a movie

32 Numerical Analysis and Strategic Comparative Analysis

321 Star Selection and Spectator Heterogeneity

(1) Star SelectionThe star selection as a critical component ofthe film investment has a huge influence on the outcome ofbox-office which has been largely ignored in past academicresearch [39] The selection of movie stars by film investorcan be divided into four strategies (in Table 2) according tothe remuneration and box-office guarantee The higher theremuneration thatmovie stars earn the larger the120583119878 and viceversa The value of 120572 and 120574 is large if movie stars can bringhigh box-office and vice versa

(2) Spectator Heterogeneity Anecdotal evidence suggests thatthe presence of superstars is not always a guarantee of successand hence a deeper study is required to analyze the potentialaudience of a movie [7] Therefore this paper considersthe film audience to be heterogeneous We only considerspectator heterogeneity rational audiences and fans Theformerrsquos proportion is 120596 and the latterrsquos share is 1-120596

It is also assumed that the film ticket price is constant p=1Let 120583119860 = 120583119872 = 1 120582=120575=005 We assume that advertising hasweak influence on film goodwill andmoviegoers so the rangeof 120572 and 120574 is small

(1) Rational audiences They lay more attention on film-making and film goodwill Therefore 120573 and 120576 have highervalues see Table 3

(2) Fans They lay emphasis on famous actor or directorTherefore 120578 has a higher value but 120573 and 120576 have lower valuessee Table 4

(3) Investment Analysis of Spectator Heterogeneity On thebasis of equilibrium solutions and numerical values we drawbar charts shown in Figure 1 The films investment strategyvaries as the rational audience and fans have different viewingrequirements for the film Studios give high investmentin film-making in the face of rational audiences But theinvestment in star is high in order to cater to the fansFirstly the studiosrsquo investment in film advertising is thesame whether for the rational audiences or fans Secondlybecause the film-making level has a great impact on word-of-mouth studios increase investment in film-making toingratiate rational audiences but economize the film-makingcosts in the face of fans Thirdly among these 4 strategies ofstar selection the film investment in strategy 3 is the highestand significantly higher than the sum of investments inadvertising and film-makingMeanwhile the film investmentin strategy 3 is several times higher than the cost of actorsin other strategies The investment in star of strategy 1 is thesecond and strategy 2 gives lowest investment in star whenfacing with the rational audiences But for fans strategy 4has the second investment to star and strategy 2 gives lowestinvestment in star No matter rational audiences or fans thestar selection in strategy 3 is the most cost-effective while thestar cost-effectiveness of strategy 2 is minimum

Discrete Dynamics in Nature and Society 5

0010203040506070809

advertising filmmaking star

Rational audiences

0

05

1

15

2

25

advertising filmmaking star

Fans

Strategy 1Strategy 2

Strategy 3Strategy 4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 1 Investment analysis of spectator heterogeneity

In fact above analysis is precisely the case of invest-ment made by film producers For example when selectingactors and actresses film producers comprehensively take thecombination of male and female protagonists into accountIn Hong Kong movies for instance ldquoaward winning actorsfrom Hong Kong usually work together with Chinese main-land second-tier actressesrdquo or ldquoChinese mainland first-tireactresses usually work together with second and third-tieractors from Hong Kong and Taiwanrdquo While consideringthe number of fans they would arrange some well-knownsecond- and third-tier stars with reasonable remuneration

322 FilmHeterogeneity and Numerical Analysis This paperdivides the film genre into new theme film and film series(eg Star Trek Pirates of the Caribbean or Fast amp Furious)Compared with new theme films films series refer to contin-uous multiset serial movies The numerical analysis of filminvestment performance is as follows

(1) New Theme Film (1) Cost analysis The movie cost underdifferent star selection strategies is shown in Figure 2 (thevertical axis is dimensionless) The investment cost underdifferent strategies increases with the proportion of rationalaudience (120596 is the proportion of rational audience 120596 isin[0 1]) The cost increment of strategy 3 is the highest andthat of strategy 4 is the lowest On the one hand the costof strategies 3 and 4 is higher than that of strategies 1 and 2when fans are the main spectator group On the other handwhen rational audience accounts for a large proportion thetotal cost of strategy 1 is higher than that of strategy 4 but thecost of strategy 2 and strategy 4 tends to approach each otherOverall the investment cost of strategy 3 is the highest andthat of strategy 2 is the lowest Nomatter what kind ofmoviesthe investment cost of rational audience is higher than that offans

(2) The number of moviegoers and the box-office analysisFigure 3 (the vertical axis is dimensionless) shows that high-paid stars contribute less to the number of moviegoers thanthe low-paid ones The reason is that over-high cost limitsfilm producersrsquo investment in high-profile stars Although thehigh popularity of stars makes a huge contribution to thenumber of moviegoers the over-high remuneration lowersstars cost performance At the same time the higher cost

02 04 06 08 10

1

2

3

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 2 Total movie cost under different star selection strategies

02 04 06 08 10

4

6

8

10

Strategy 1Strategy 2

Strategy 3Strategy 4

2

Figure 3 Moviegoers of new theme film under different starselection strategies

performance makes producers increase the star investmentand also increase the number of moviegoers Bankable starstruly guarantee the box-office and the influence of such starson the number of moviegoers is great As the proportion ofrational audience increases this influence is more significantIt can be interpreted that rational audience always pay moreattention to actors acting skills and film-making quality And

6 Discrete Dynamics in Nature and Society

box-office guarantee means getting the audiencersquos approvalin the aspects of directors acting skills script selection etcThe audience loyalty to bankable stars is higher and then thenumber of moviegoers is more

In Figure 3 the biggest number of moviegoers is instrategy 3 which has the participation of the low-paid butbankable stars so-called low-profile stars with real strengthThese stars own good acting skills loyal audience relativelyreasonable remuneration and high cost performance There-fore strategy 3 has a relatively strong influence on both fansand the rational audience and earns more expected profitsthan other strategies The smallest number of moviegoersis in strategy 2 which has the participation of the high-paid but with no box-office guaranteed actors Despite suchstars having high popularity their acting skills have beenquestioned and criticized by moviegoers Generally themovie they are involved in has no guarantee at the box-officeand its online word-of-mouth is also poor

It is generally recognized that fans are an importantcriterion for film producers to choose actors But Figure 5shows that rational audiences are the main guarantee of box-office rather than fans Due to that film producers investmentin rational audiences is higher than that in fans the marketperformance of rational audiences is better than that of fansThe number of moviegoers is directly proportional to theratio of rational audience and is inversely proportional to theratio of fans So it is easy to understand the poor box-officeperformance of movies starring high-paid ldquolittle fresh meatrdquowho have a huge number of fans but no box-office guaranteeFor actors who have no box-office guarantee as the numberof fans decreases moviegoers in strategy 2 with high-paidactors will outnumber strategy 4 with low-paid actors whichis mainly because of the impact of star popularity on themovies reputation

Meanwhile with the development of network film pro-ducers paymore andmore attention tomoviegoersrsquo opinionsFor example during the preparation of many movies as aresult of fansrsquo doubts and dissatisfaction with the star lineupthe incident of changing actors occurs frequently This alsoshows film producersrsquo expectations for moviegoers and box-office and their consideration about starsrsquo impact on filmreputation when making investment decisions At the sametime with the changes of online word-of-mouth after themovie is released the reputation of stars changes accordinglySome stars may surge in popularity because of their excellentacting skills which further enhances the reputation of themovie some actors are questioned because of poor actingskills resulting in damage to the movie reputation and box-office slump

(3) Revenue analysis The final revenue of a movie isaffected by box-office and investment costs This paperfocuses on film investment decision-making and the ulti-mate goal is tomaximize themoviersquos revenueWe assume thatthe revenues of all strategies are positive and the vertical axisis dimensionless Figure 4 shows that the higher the rationalaudience ratio the higher the movie revenue Because whenthe film investor expects a movie to be positive and supposesthat the rational audience is influenced by the word-of-mouth with the increase of moviegoers the accumulation

02 04 06 08 10

2

3

5

6

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 4 Revenue of new theme film under different strategies

02 04 06 08 10

4

6

8

10

2

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 5 Moviegoers of film series under different star selectionstrategies

of online word-of-mouth will increase the possibility ofaudiencersquos going to cinema thus increasing the film revenueIt is easy to understand that corresponding to the numberof moviegoers revenues of movies played by bankable starsare higher than that with no box-office guaranteed stars Inaddition under costrsquos influence revenues of movies playedby low-paid actors are higher than that of high-paid actors

(2) Film Series Film series have a high reputation in the earlystage of film release due to the accumulation of early seriesHigh film reputation does not change the investment strategyso the investment cost of film series is consistent with that ofa new thememovie As shown in Figures 5 and 6 (the verticalaxis is dimensionless) influenced by accumulated popularitythe number of film seriesrsquo moviegoers and its revenues arehigher than that of a new theme movie That is why filmproducers prefer giving investment in sequel movies ratherthan new theme movies when there is a good response to theserialmoviesTherefore there are alwaysmovies based onTVdramas variety shows and popular online novels Besides itis also easy to understand that the same story (eg Journeyto the West) is reshot over and over again All the above are

Discrete Dynamics in Nature and Society 7

02 04 06 08 10

2

3

5

6

4

7

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 6 Revenue of film series under different star selectionstrategies

the cases in which film producers take advantage of the highreputation accumulated before

Similarly the audience keeping high loyalty to some actoror director (being a fan of the star or director) on the onehand is the recognition of the directors directing skills oractors acting skills and on the other hand the director oractors reputation that accumulated over a long period oftime gives them a box-office guarantee in the mind of spec-tator Therefore the relationship between actors directorsand movies should be mutual promotion when an actorspopularity and acting skills or directors directing ability havehigh-performance in online word-of-mouth and box-officethen the movie will further enhance and consolidate theactors or the directors popularity

4 System Dynamics Analysis of Film Goodwilland Box-Office

41 The System Dynamics Model System dynamics is awell-established methodology to model and understand thebehavior of complex systems and it has been extensively usedfor modeling the dynamic behavior of complex nonlinearsystems [40 41] Based on the above filmrsquos goodwill modelthe SD model of film goodwill reflects the dynamic impactof advertising film-making and star power on film perfor-mance The advertising and star power factors have directeffects on the box-office and the film-making effort indirectlyinfluences the box-office through film goodwill Then thebox-office in turn affects the three factors Figure 7 shows thestock and flowdiagram for the systemdynamicsmodel of filmgoodwill by SD software-Vensim version 71

42 The System Dynamics Analysis According to Chen andYin [42] movies have relatively short life cycles and theaverage exposure time of a movie is approximately onemonth Based on SD model in Section 41 and equilibriumsolutions in Section 3 we will analyze four star selectionstrategies of new theme film by SD simulation Then we getthe box-office trend of rational audiences and fans duringthe release period as shown in Figures 8 and 9 (the vertical

axis of box-office is dimensionless) In Figures 3 and 8 forrational moviegoers strategy 3 has a higher investment instars who are reasonably paid with box-office guarantee andthe film-making is excellent Compared with other moviesstrategy 3 can have a good performance at the early stageof release time and the potential development is great Asa result it has considerable returns on investment Movies(Strategies 1 2 and 4) are ordinary in performance Exceptfor movies (Strategy 1) played by high-paid bankable starswhose performance is slightly better the box-office of othermovies (Strategies 2 and 4) is close In Figures 2 and 9 forfans even though their idols act in the movies they do notpay much for the low-quality film-making Particularly instrategies 1 and 2 due to bad word-of-mouth caused by lowinvestment in film-making movies with high popularity starscannot achieve good performance if just relying on fans effectFor movies with high investment in film-making obviouslybankable stars are far more attractive to audience than thatwith no box-office guarantee But generally the performanceof movies with high investment in film-making is better thanthat with low investment in film-making

In summary in order to maximize the profit fromProposition 1 film producers choose different types of starsaccording to different needs of moviegoers and thus makedifferent investment decisions However returns of filminvestment follow the principle that high investment getshigh returns Among film investment strategies strategy 3has the highest investment most moviegoers and highestreturns while strategy 2 has the lowest investment leastmoviegoers and least returns

Compared with new theme film what film series reflectin the SD simulation is nothing but the fact that initial valueof simulated box-office is higher Other performances of filmseries in the release period are consistent with new themefilm So the SD analysis of film series is omitted in this paperBecause of the accumulated high reputation the box-office offilm series is always better than that of new theme film

5 Concluding Remarks andManagerial Implications

This paper considers the joint effects of advertising film-making and star power on film reputation the numberof moviegoers and box-office We consider the investmentdecision of a movie made by studios or investors and developa goodwill model and system dynamic model which allowus to disentangle advertising film-making and star powereffects The results are proved as follows

Firstly the film producersrsquo investment in advertisingfilm-making and star power are positively correlated withtheir contribution to film reputation and the number ofmoviegoers but negatively correlatedwith the cost coefficientof three factors The film producer will increasingly layemphasis on investing in advertising such as the release con-ference titbits trailers and show tours to absorbmoviegoersrsquoattention The film producer focuses on investing in film-making when film quality has a great impact on the moviesreputation and the audiences viewing decision For invest-ment in stars the film producer paysmore attention to higher

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

Discrete Dynamics in Nature and Society 5

0010203040506070809

advertising filmmaking star

Rational audiences

0

05

1

15

2

25

advertising filmmaking star

Fans

Strategy 1Strategy 2

Strategy 3Strategy 4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 1 Investment analysis of spectator heterogeneity

In fact above analysis is precisely the case of invest-ment made by film producers For example when selectingactors and actresses film producers comprehensively take thecombination of male and female protagonists into accountIn Hong Kong movies for instance ldquoaward winning actorsfrom Hong Kong usually work together with Chinese main-land second-tier actressesrdquo or ldquoChinese mainland first-tireactresses usually work together with second and third-tieractors from Hong Kong and Taiwanrdquo While consideringthe number of fans they would arrange some well-knownsecond- and third-tier stars with reasonable remuneration

322 FilmHeterogeneity and Numerical Analysis This paperdivides the film genre into new theme film and film series(eg Star Trek Pirates of the Caribbean or Fast amp Furious)Compared with new theme films films series refer to contin-uous multiset serial movies The numerical analysis of filminvestment performance is as follows

(1) New Theme Film (1) Cost analysis The movie cost underdifferent star selection strategies is shown in Figure 2 (thevertical axis is dimensionless) The investment cost underdifferent strategies increases with the proportion of rationalaudience (120596 is the proportion of rational audience 120596 isin[0 1]) The cost increment of strategy 3 is the highest andthat of strategy 4 is the lowest On the one hand the costof strategies 3 and 4 is higher than that of strategies 1 and 2when fans are the main spectator group On the other handwhen rational audience accounts for a large proportion thetotal cost of strategy 1 is higher than that of strategy 4 but thecost of strategy 2 and strategy 4 tends to approach each otherOverall the investment cost of strategy 3 is the highest andthat of strategy 2 is the lowest Nomatter what kind ofmoviesthe investment cost of rational audience is higher than that offans

(2) The number of moviegoers and the box-office analysisFigure 3 (the vertical axis is dimensionless) shows that high-paid stars contribute less to the number of moviegoers thanthe low-paid ones The reason is that over-high cost limitsfilm producersrsquo investment in high-profile stars Although thehigh popularity of stars makes a huge contribution to thenumber of moviegoers the over-high remuneration lowersstars cost performance At the same time the higher cost

02 04 06 08 10

1

2

3

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 2 Total movie cost under different star selection strategies

02 04 06 08 10

4

6

8

10

Strategy 1Strategy 2

Strategy 3Strategy 4

2

Figure 3 Moviegoers of new theme film under different starselection strategies

performance makes producers increase the star investmentand also increase the number of moviegoers Bankable starstruly guarantee the box-office and the influence of such starson the number of moviegoers is great As the proportion ofrational audience increases this influence is more significantIt can be interpreted that rational audience always pay moreattention to actors acting skills and film-making quality And

6 Discrete Dynamics in Nature and Society

box-office guarantee means getting the audiencersquos approvalin the aspects of directors acting skills script selection etcThe audience loyalty to bankable stars is higher and then thenumber of moviegoers is more

In Figure 3 the biggest number of moviegoers is instrategy 3 which has the participation of the low-paid butbankable stars so-called low-profile stars with real strengthThese stars own good acting skills loyal audience relativelyreasonable remuneration and high cost performance There-fore strategy 3 has a relatively strong influence on both fansand the rational audience and earns more expected profitsthan other strategies The smallest number of moviegoersis in strategy 2 which has the participation of the high-paid but with no box-office guaranteed actors Despite suchstars having high popularity their acting skills have beenquestioned and criticized by moviegoers Generally themovie they are involved in has no guarantee at the box-officeand its online word-of-mouth is also poor

It is generally recognized that fans are an importantcriterion for film producers to choose actors But Figure 5shows that rational audiences are the main guarantee of box-office rather than fans Due to that film producers investmentin rational audiences is higher than that in fans the marketperformance of rational audiences is better than that of fansThe number of moviegoers is directly proportional to theratio of rational audience and is inversely proportional to theratio of fans So it is easy to understand the poor box-officeperformance of movies starring high-paid ldquolittle fresh meatrdquowho have a huge number of fans but no box-office guaranteeFor actors who have no box-office guarantee as the numberof fans decreases moviegoers in strategy 2 with high-paidactors will outnumber strategy 4 with low-paid actors whichis mainly because of the impact of star popularity on themovies reputation

Meanwhile with the development of network film pro-ducers paymore andmore attention tomoviegoersrsquo opinionsFor example during the preparation of many movies as aresult of fansrsquo doubts and dissatisfaction with the star lineupthe incident of changing actors occurs frequently This alsoshows film producersrsquo expectations for moviegoers and box-office and their consideration about starsrsquo impact on filmreputation when making investment decisions At the sametime with the changes of online word-of-mouth after themovie is released the reputation of stars changes accordinglySome stars may surge in popularity because of their excellentacting skills which further enhances the reputation of themovie some actors are questioned because of poor actingskills resulting in damage to the movie reputation and box-office slump

(3) Revenue analysis The final revenue of a movie isaffected by box-office and investment costs This paperfocuses on film investment decision-making and the ulti-mate goal is tomaximize themoviersquos revenueWe assume thatthe revenues of all strategies are positive and the vertical axisis dimensionless Figure 4 shows that the higher the rationalaudience ratio the higher the movie revenue Because whenthe film investor expects a movie to be positive and supposesthat the rational audience is influenced by the word-of-mouth with the increase of moviegoers the accumulation

02 04 06 08 10

2

3

5

6

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 4 Revenue of new theme film under different strategies

02 04 06 08 10

4

6

8

10

2

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 5 Moviegoers of film series under different star selectionstrategies

of online word-of-mouth will increase the possibility ofaudiencersquos going to cinema thus increasing the film revenueIt is easy to understand that corresponding to the numberof moviegoers revenues of movies played by bankable starsare higher than that with no box-office guaranteed stars Inaddition under costrsquos influence revenues of movies playedby low-paid actors are higher than that of high-paid actors

(2) Film Series Film series have a high reputation in the earlystage of film release due to the accumulation of early seriesHigh film reputation does not change the investment strategyso the investment cost of film series is consistent with that ofa new thememovie As shown in Figures 5 and 6 (the verticalaxis is dimensionless) influenced by accumulated popularitythe number of film seriesrsquo moviegoers and its revenues arehigher than that of a new theme movie That is why filmproducers prefer giving investment in sequel movies ratherthan new theme movies when there is a good response to theserialmoviesTherefore there are alwaysmovies based onTVdramas variety shows and popular online novels Besides itis also easy to understand that the same story (eg Journeyto the West) is reshot over and over again All the above are

Discrete Dynamics in Nature and Society 7

02 04 06 08 10

2

3

5

6

4

7

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 6 Revenue of film series under different star selectionstrategies

the cases in which film producers take advantage of the highreputation accumulated before

Similarly the audience keeping high loyalty to some actoror director (being a fan of the star or director) on the onehand is the recognition of the directors directing skills oractors acting skills and on the other hand the director oractors reputation that accumulated over a long period oftime gives them a box-office guarantee in the mind of spec-tator Therefore the relationship between actors directorsand movies should be mutual promotion when an actorspopularity and acting skills or directors directing ability havehigh-performance in online word-of-mouth and box-officethen the movie will further enhance and consolidate theactors or the directors popularity

4 System Dynamics Analysis of Film Goodwilland Box-Office

41 The System Dynamics Model System dynamics is awell-established methodology to model and understand thebehavior of complex systems and it has been extensively usedfor modeling the dynamic behavior of complex nonlinearsystems [40 41] Based on the above filmrsquos goodwill modelthe SD model of film goodwill reflects the dynamic impactof advertising film-making and star power on film perfor-mance The advertising and star power factors have directeffects on the box-office and the film-making effort indirectlyinfluences the box-office through film goodwill Then thebox-office in turn affects the three factors Figure 7 shows thestock and flowdiagram for the systemdynamicsmodel of filmgoodwill by SD software-Vensim version 71

42 The System Dynamics Analysis According to Chen andYin [42] movies have relatively short life cycles and theaverage exposure time of a movie is approximately onemonth Based on SD model in Section 41 and equilibriumsolutions in Section 3 we will analyze four star selectionstrategies of new theme film by SD simulation Then we getthe box-office trend of rational audiences and fans duringthe release period as shown in Figures 8 and 9 (the vertical

axis of box-office is dimensionless) In Figures 3 and 8 forrational moviegoers strategy 3 has a higher investment instars who are reasonably paid with box-office guarantee andthe film-making is excellent Compared with other moviesstrategy 3 can have a good performance at the early stageof release time and the potential development is great Asa result it has considerable returns on investment Movies(Strategies 1 2 and 4) are ordinary in performance Exceptfor movies (Strategy 1) played by high-paid bankable starswhose performance is slightly better the box-office of othermovies (Strategies 2 and 4) is close In Figures 2 and 9 forfans even though their idols act in the movies they do notpay much for the low-quality film-making Particularly instrategies 1 and 2 due to bad word-of-mouth caused by lowinvestment in film-making movies with high popularity starscannot achieve good performance if just relying on fans effectFor movies with high investment in film-making obviouslybankable stars are far more attractive to audience than thatwith no box-office guarantee But generally the performanceof movies with high investment in film-making is better thanthat with low investment in film-making

In summary in order to maximize the profit fromProposition 1 film producers choose different types of starsaccording to different needs of moviegoers and thus makedifferent investment decisions However returns of filminvestment follow the principle that high investment getshigh returns Among film investment strategies strategy 3has the highest investment most moviegoers and highestreturns while strategy 2 has the lowest investment leastmoviegoers and least returns

Compared with new theme film what film series reflectin the SD simulation is nothing but the fact that initial valueof simulated box-office is higher Other performances of filmseries in the release period are consistent with new themefilm So the SD analysis of film series is omitted in this paperBecause of the accumulated high reputation the box-office offilm series is always better than that of new theme film

5 Concluding Remarks andManagerial Implications

This paper considers the joint effects of advertising film-making and star power on film reputation the numberof moviegoers and box-office We consider the investmentdecision of a movie made by studios or investors and developa goodwill model and system dynamic model which allowus to disentangle advertising film-making and star powereffects The results are proved as follows

Firstly the film producersrsquo investment in advertisingfilm-making and star power are positively correlated withtheir contribution to film reputation and the number ofmoviegoers but negatively correlatedwith the cost coefficientof three factors The film producer will increasingly layemphasis on investing in advertising such as the release con-ference titbits trailers and show tours to absorbmoviegoersrsquoattention The film producer focuses on investing in film-making when film quality has a great impact on the moviesreputation and the audiences viewing decision For invest-ment in stars the film producer paysmore attention to higher

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

6 Discrete Dynamics in Nature and Society

box-office guarantee means getting the audiencersquos approvalin the aspects of directors acting skills script selection etcThe audience loyalty to bankable stars is higher and then thenumber of moviegoers is more

In Figure 3 the biggest number of moviegoers is instrategy 3 which has the participation of the low-paid butbankable stars so-called low-profile stars with real strengthThese stars own good acting skills loyal audience relativelyreasonable remuneration and high cost performance There-fore strategy 3 has a relatively strong influence on both fansand the rational audience and earns more expected profitsthan other strategies The smallest number of moviegoersis in strategy 2 which has the participation of the high-paid but with no box-office guaranteed actors Despite suchstars having high popularity their acting skills have beenquestioned and criticized by moviegoers Generally themovie they are involved in has no guarantee at the box-officeand its online word-of-mouth is also poor

It is generally recognized that fans are an importantcriterion for film producers to choose actors But Figure 5shows that rational audiences are the main guarantee of box-office rather than fans Due to that film producers investmentin rational audiences is higher than that in fans the marketperformance of rational audiences is better than that of fansThe number of moviegoers is directly proportional to theratio of rational audience and is inversely proportional to theratio of fans So it is easy to understand the poor box-officeperformance of movies starring high-paid ldquolittle fresh meatrdquowho have a huge number of fans but no box-office guaranteeFor actors who have no box-office guarantee as the numberof fans decreases moviegoers in strategy 2 with high-paidactors will outnumber strategy 4 with low-paid actors whichis mainly because of the impact of star popularity on themovies reputation

Meanwhile with the development of network film pro-ducers paymore andmore attention tomoviegoersrsquo opinionsFor example during the preparation of many movies as aresult of fansrsquo doubts and dissatisfaction with the star lineupthe incident of changing actors occurs frequently This alsoshows film producersrsquo expectations for moviegoers and box-office and their consideration about starsrsquo impact on filmreputation when making investment decisions At the sametime with the changes of online word-of-mouth after themovie is released the reputation of stars changes accordinglySome stars may surge in popularity because of their excellentacting skills which further enhances the reputation of themovie some actors are questioned because of poor actingskills resulting in damage to the movie reputation and box-office slump

(3) Revenue analysis The final revenue of a movie isaffected by box-office and investment costs This paperfocuses on film investment decision-making and the ulti-mate goal is tomaximize themoviersquos revenueWe assume thatthe revenues of all strategies are positive and the vertical axisis dimensionless Figure 4 shows that the higher the rationalaudience ratio the higher the movie revenue Because whenthe film investor expects a movie to be positive and supposesthat the rational audience is influenced by the word-of-mouth with the increase of moviegoers the accumulation

02 04 06 08 10

2

3

5

6

4

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 4 Revenue of new theme film under different strategies

02 04 06 08 10

4

6

8

10

2

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 5 Moviegoers of film series under different star selectionstrategies

of online word-of-mouth will increase the possibility ofaudiencersquos going to cinema thus increasing the film revenueIt is easy to understand that corresponding to the numberof moviegoers revenues of movies played by bankable starsare higher than that with no box-office guaranteed stars Inaddition under costrsquos influence revenues of movies playedby low-paid actors are higher than that of high-paid actors

(2) Film Series Film series have a high reputation in the earlystage of film release due to the accumulation of early seriesHigh film reputation does not change the investment strategyso the investment cost of film series is consistent with that ofa new thememovie As shown in Figures 5 and 6 (the verticalaxis is dimensionless) influenced by accumulated popularitythe number of film seriesrsquo moviegoers and its revenues arehigher than that of a new theme movie That is why filmproducers prefer giving investment in sequel movies ratherthan new theme movies when there is a good response to theserialmoviesTherefore there are alwaysmovies based onTVdramas variety shows and popular online novels Besides itis also easy to understand that the same story (eg Journeyto the West) is reshot over and over again All the above are

Discrete Dynamics in Nature and Society 7

02 04 06 08 10

2

3

5

6

4

7

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 6 Revenue of film series under different star selectionstrategies

the cases in which film producers take advantage of the highreputation accumulated before

Similarly the audience keeping high loyalty to some actoror director (being a fan of the star or director) on the onehand is the recognition of the directors directing skills oractors acting skills and on the other hand the director oractors reputation that accumulated over a long period oftime gives them a box-office guarantee in the mind of spec-tator Therefore the relationship between actors directorsand movies should be mutual promotion when an actorspopularity and acting skills or directors directing ability havehigh-performance in online word-of-mouth and box-officethen the movie will further enhance and consolidate theactors or the directors popularity

4 System Dynamics Analysis of Film Goodwilland Box-Office

41 The System Dynamics Model System dynamics is awell-established methodology to model and understand thebehavior of complex systems and it has been extensively usedfor modeling the dynamic behavior of complex nonlinearsystems [40 41] Based on the above filmrsquos goodwill modelthe SD model of film goodwill reflects the dynamic impactof advertising film-making and star power on film perfor-mance The advertising and star power factors have directeffects on the box-office and the film-making effort indirectlyinfluences the box-office through film goodwill Then thebox-office in turn affects the three factors Figure 7 shows thestock and flowdiagram for the systemdynamicsmodel of filmgoodwill by SD software-Vensim version 71

42 The System Dynamics Analysis According to Chen andYin [42] movies have relatively short life cycles and theaverage exposure time of a movie is approximately onemonth Based on SD model in Section 41 and equilibriumsolutions in Section 3 we will analyze four star selectionstrategies of new theme film by SD simulation Then we getthe box-office trend of rational audiences and fans duringthe release period as shown in Figures 8 and 9 (the vertical

axis of box-office is dimensionless) In Figures 3 and 8 forrational moviegoers strategy 3 has a higher investment instars who are reasonably paid with box-office guarantee andthe film-making is excellent Compared with other moviesstrategy 3 can have a good performance at the early stageof release time and the potential development is great Asa result it has considerable returns on investment Movies(Strategies 1 2 and 4) are ordinary in performance Exceptfor movies (Strategy 1) played by high-paid bankable starswhose performance is slightly better the box-office of othermovies (Strategies 2 and 4) is close In Figures 2 and 9 forfans even though their idols act in the movies they do notpay much for the low-quality film-making Particularly instrategies 1 and 2 due to bad word-of-mouth caused by lowinvestment in film-making movies with high popularity starscannot achieve good performance if just relying on fans effectFor movies with high investment in film-making obviouslybankable stars are far more attractive to audience than thatwith no box-office guarantee But generally the performanceof movies with high investment in film-making is better thanthat with low investment in film-making

In summary in order to maximize the profit fromProposition 1 film producers choose different types of starsaccording to different needs of moviegoers and thus makedifferent investment decisions However returns of filminvestment follow the principle that high investment getshigh returns Among film investment strategies strategy 3has the highest investment most moviegoers and highestreturns while strategy 2 has the lowest investment leastmoviegoers and least returns

Compared with new theme film what film series reflectin the SD simulation is nothing but the fact that initial valueof simulated box-office is higher Other performances of filmseries in the release period are consistent with new themefilm So the SD analysis of film series is omitted in this paperBecause of the accumulated high reputation the box-office offilm series is always better than that of new theme film

5 Concluding Remarks andManagerial Implications

This paper considers the joint effects of advertising film-making and star power on film reputation the numberof moviegoers and box-office We consider the investmentdecision of a movie made by studios or investors and developa goodwill model and system dynamic model which allowus to disentangle advertising film-making and star powereffects The results are proved as follows

Firstly the film producersrsquo investment in advertisingfilm-making and star power are positively correlated withtheir contribution to film reputation and the number ofmoviegoers but negatively correlatedwith the cost coefficientof three factors The film producer will increasingly layemphasis on investing in advertising such as the release con-ference titbits trailers and show tours to absorbmoviegoersrsquoattention The film producer focuses on investing in film-making when film quality has a great impact on the moviesreputation and the audiences viewing decision For invest-ment in stars the film producer paysmore attention to higher

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

Discrete Dynamics in Nature and Society 7

02 04 06 08 10

2

3

5

6

4

7

Strategy 1Strategy 2

Strategy 3Strategy 4

Figure 6 Revenue of film series under different star selectionstrategies

the cases in which film producers take advantage of the highreputation accumulated before

Similarly the audience keeping high loyalty to some actoror director (being a fan of the star or director) on the onehand is the recognition of the directors directing skills oractors acting skills and on the other hand the director oractors reputation that accumulated over a long period oftime gives them a box-office guarantee in the mind of spec-tator Therefore the relationship between actors directorsand movies should be mutual promotion when an actorspopularity and acting skills or directors directing ability havehigh-performance in online word-of-mouth and box-officethen the movie will further enhance and consolidate theactors or the directors popularity

4 System Dynamics Analysis of Film Goodwilland Box-Office

41 The System Dynamics Model System dynamics is awell-established methodology to model and understand thebehavior of complex systems and it has been extensively usedfor modeling the dynamic behavior of complex nonlinearsystems [40 41] Based on the above filmrsquos goodwill modelthe SD model of film goodwill reflects the dynamic impactof advertising film-making and star power on film perfor-mance The advertising and star power factors have directeffects on the box-office and the film-making effort indirectlyinfluences the box-office through film goodwill Then thebox-office in turn affects the three factors Figure 7 shows thestock and flowdiagram for the systemdynamicsmodel of filmgoodwill by SD software-Vensim version 71

42 The System Dynamics Analysis According to Chen andYin [42] movies have relatively short life cycles and theaverage exposure time of a movie is approximately onemonth Based on SD model in Section 41 and equilibriumsolutions in Section 3 we will analyze four star selectionstrategies of new theme film by SD simulation Then we getthe box-office trend of rational audiences and fans duringthe release period as shown in Figures 8 and 9 (the vertical

axis of box-office is dimensionless) In Figures 3 and 8 forrational moviegoers strategy 3 has a higher investment instars who are reasonably paid with box-office guarantee andthe film-making is excellent Compared with other moviesstrategy 3 can have a good performance at the early stageof release time and the potential development is great Asa result it has considerable returns on investment Movies(Strategies 1 2 and 4) are ordinary in performance Exceptfor movies (Strategy 1) played by high-paid bankable starswhose performance is slightly better the box-office of othermovies (Strategies 2 and 4) is close In Figures 2 and 9 forfans even though their idols act in the movies they do notpay much for the low-quality film-making Particularly instrategies 1 and 2 due to bad word-of-mouth caused by lowinvestment in film-making movies with high popularity starscannot achieve good performance if just relying on fans effectFor movies with high investment in film-making obviouslybankable stars are far more attractive to audience than thatwith no box-office guarantee But generally the performanceof movies with high investment in film-making is better thanthat with low investment in film-making

In summary in order to maximize the profit fromProposition 1 film producers choose different types of starsaccording to different needs of moviegoers and thus makedifferent investment decisions However returns of filminvestment follow the principle that high investment getshigh returns Among film investment strategies strategy 3has the highest investment most moviegoers and highestreturns while strategy 2 has the lowest investment leastmoviegoers and least returns

Compared with new theme film what film series reflectin the SD simulation is nothing but the fact that initial valueof simulated box-office is higher Other performances of filmseries in the release period are consistent with new themefilm So the SD analysis of film series is omitted in this paperBecause of the accumulated high reputation the box-office offilm series is always better than that of new theme film

5 Concluding Remarks andManagerial Implications

This paper considers the joint effects of advertising film-making and star power on film reputation the numberof moviegoers and box-office We consider the investmentdecision of a movie made by studios or investors and developa goodwill model and system dynamic model which allowus to disentangle advertising film-making and star powereffects The results are proved as follows

Firstly the film producersrsquo investment in advertisingfilm-making and star power are positively correlated withtheir contribution to film reputation and the number ofmoviegoers but negatively correlatedwith the cost coefficientof three factors The film producer will increasingly layemphasis on investing in advertising such as the release con-ference titbits trailers and show tours to absorbmoviegoersrsquoattention The film producer focuses on investing in film-making when film quality has a great impact on the moviesreputation and the audiences viewing decision For invest-ment in stars the film producer paysmore attention to higher

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

8 Discrete Dynamics in Nature and Society

Goodwill

goodwill decayrate

box-office

stars contributionrate to box-office

goodwillscontribution rate to

box-office

ads influencecoefficient

filmmakingsinfluence coefficient

Advertising effort

Filmmaking effort

Star power effort

stars influencecoefficient

goodwill effect rate

ads contributionrate to box-office

Figure 7 Stock and flow diagram for film goodwill

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

20

15

5

00 2 4 6 8

10

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 8 Box-office trend of rational audience against film releasetime

20

15

5

00 2 4 6 8

10

box-office Strategy 1box-office Strategy 2box-office Strategy 3box-office Strategy 4

10 12 14 16 18 20 22 24 26 28 30Time (Day)

Figure 9 Box-office trend of fans against film release time

cost-performance stars who have reasonable remunerationgood acting skills and big box-office guarantee

Secondly the film producer makes different decisions tomeet different audiencesrsquo viewing requirements For rationalaudience more attention is paid to film-making investmentbut for fans more attention is paid to investment in starsWhether it is a new theme film or film series the filminvestment cost for rational audience is higher than thatfor fans Correspondingly rational audience also contributesmore box-office returns

Thirdly by the principle that high investment yields highreturns movies played by stars with reasonable remunerationand good acting skills have the highest investment costCorrespondingly these movies have the largest number ofmoviegoers and box-office returns When movies played bystars with over-high remuneration and poor acting skills havethe lowest investment correspondingly those movies getthe least moviegoers and box-office returns When rationalaudiences outnumber fans despite the high remunerationboth moviegoers and box-office of movies acted by bankablestars are more than that acted by stars with no box-officeguarantees

Fourthly the box-office will increase gradually over filmrelease time For the movies acted by bankable stars who arenot well-known with low remuneration they have excellentfilm-making quality and show the best performance There-fore they are most worthy of investment For those moviesacted by well-known stars but with no box-office guaranteesthey show the worst performance and are least worthy ofinvestment Accordingly such poor quality movies may yielddisappointing box-office and reputation

Finally compared with new theme film film series enablea better performance (eg number of moviegoers box-officerevenues) because of high reputation This is the fundamentalreason why the film producers love serial movie

The research findings about the film investment decisionare based on the goal ofmaximizing filmproducersrsquo profits Inreality there are many random factors except for advertisingfilm-making and star power affecting audiencersquos viewingdecision However this paper can provide instructions formaking investment decisions in film industry fromamanage-rial perspective Compared with fans the rational audiencecontributes more to a movies box-office Compared withpopularity bankable stars contribute more to a moviesreturns And compared with new theme film film seriesyields higher profits

Appendix

We solve the optimal control question and obtain feed-back equilibrium solutions using backwards induction We

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

Discrete Dynamics in Nature and Society 9

suppose that the optimal profit function of a movie is 119881(119866)Then the Hamilton-Jacobi-Bellman (HJB) equation must besatisfied

120582119881 (119866) = max [119901 (120590119878 + 120574119860 + 120576119866) minus 1205831198602 1198602 minus 1205831198722 1198722

minus 1205831198782 1198782 + 1198811015840 (119866) (120572119860 + 120573119872 + 120578119878 minus 120575119866)](A1)

where 1198811015840(119866) = 119889119881(119866)119889119866 Maximization of the right-handside of the HJB equation yields

119860lowast (1198811015840) = 120574119901120583119860 +

1205721198811015840120583119860 (A2)

119872lowast (1198811015840) = 1205731198811015840120583119872 (A3)

119878lowast (1198811015840) = 120590119901120583119878 +

1205781198811015840120583119878 (A4)

It is easy to know Hessian Matrix of (A1) is negative-definite Equations (A2)-(A4) are the optimum solutions tomaximize the profit in (A1) Substituting (A2)-(A4) into(A1) we obtain120582119881 (119866)= 119901(120576119866 + 1205721198811015840

120583119860 + 120574119901120583119860 +

1205781198811015840120583119878 + 120590119901

120583119878 )

+ 1198811015840 (12057221198811015840120583119860 + 120572119901

120583119860 +12057321198811015840120583119872 + 12057821198811015840

120583119878 + 120578119901120583119878 minus 120575119866)

minus 1205831198602 (1205721198811015840120583119860 + 120574119901

120583119860)2

minus 120573211988110158402120583119872

minus 1205831198782 (1205781198811015840120583119878 + 120590119901

120583119878 )2

(A5)

We shall show that linear optimal value functions satisfy(A5) Hence we define

119881 (119866) = 1198901119866 + 1198902 (A6)where 1198901 and 1198902 are constants

By using the method of undetermined coefficients weobtain

1198901 = 120576119901120575 + 120582 (A7)

1198902 = 120576119901120575 + 120582 [120572119901120583119860 +

1205722120576119901(120575 + 120582) 120583119860 +

1205732120576119901(120575 + 120582) 120583119872 + 120578119901

120583119878+ 1205782120576119901(120575 + 120582) 120583119878] + 119901[120574119901120583119860 +

120572120576119901(120575 + 120582) 120583119860 +

120590119901120583119878

+ 120576120578119901(120575 + 120582) 120583119878 ] minus

1205831198602 [120574119901120583119860 +120572120576119901

(120575 + 120582) 120583119860]2

minus 1205732120576211990122 (120575 + 120582)2 120583119872 minus 1205831198782 [120590119901120583119878 +

120578120576119901(120575 + 120582) 120583119878 ]

2

(A8)

Substituting (A7)-(A8) into (A6) we get

1198811015840 = 120576119901120575 + 120582 (A9)

Then substituting (A9) into (A2)-(A4) we also obtain(4)-(6) Finally substituting (4)-(6) into (A1) and get (7)

This concludes the proof

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors gratefully acknowledge support from NationalNatural Science Foundation of China (Project No 71571117)and Innovation Method Fund of China (Project No2016IM010400)

References

[1] D Delen R Sharda and P Kumar ldquoMovie forecast Guru AWeb-based DSS for Hollywood managersrdquo Decision SupportSystems vol 43 no 4 pp 1151ndash1170 2007

[2] S K Schwartz Investing in the big screen can be a profitablestory httpswwwcnbccomid39342145 2010

[3] K J Lee andW Chang ldquoBayesian belief network for box-officeperformance A case study on Korean moviesrdquo Expert Systemswith Applications vol 36 no 1 pp 280ndash291 2009

[4] A De Vany and W D Walls ldquoBose-einstein dynamics andadaptive contracting in the motion picture industryrdquo EconomicJournal vol 106 no 439 pp 1493ndash1514 1996

[5] A De Vany andWDWalls ldquoDoesHollywoodMake TooManyR-Rated Movies Risk Stochastic Dominance and the Illusionof Expectationrdquo Journal of Business vol 75 no 3 pp 425ndash4512002

[6] A De Vany and W D Walls ldquoMotion picture profit the stableParetian hypothesis and the curse of the superstarrdquo Journal ofEconomic Dynamics amp Control vol 28 no 6 pp 1035ndash10572004

[7] E Montanes A Suarez-Vazquez and J R Quevedo ldquoOrdinalclassificationregression for analyzing the influence of super-stars on spectators in cinema marketingrdquo Expert Systems withApplications vol 41 no 18 pp 8101ndash8111 2014

[8] W D Walls ldquoChapter 8ndashbestsellers and blockbusters moviesmusic and booksrdquo in Handbook of the Economics of Art ampCulture vol 2 pp 185ndash213 2014

[9] J EliashbergA Elberse andMAAM Leenders ldquoThemotionpicture industry Critical issues in practice current researchand new research directionsrdquo Marketing Science vol 25 no 6pp 638ndash661 2006

[10] L Zhang J Luo and S Yang ldquoForecasting box office revenue ofmovies with BP neural networkrdquo Expert Systems with Applica-tions vol 36 no 3 pp 6580ndash6587 2009

10 Discrete Dynamics in Nature and Society

[11] J Xiao X Li S Chen X Zhao and M Xu ldquoAn inside lookinto the complexity of box-office revenue prediction in chinardquoInternational Journal of Distributed Sensor Networks vol 13 no1 pp 1ndash14 2017

[12] T Hennig-Thurau M B Houston and G Walsh ldquoDeter-minants of motion picture box office and profitability aninterrelationship approachrdquo Review of Managerial Science vol1 no 1 pp 65ndash92 2007

[13] F S Zufryden ldquoLinking advertising to box office performanceof new film releases - A marketing planning modelrdquo Journal ofAdvertising Research vol 36 no 4 pp 29ndash41 1996

[14] A Elberse and J Eliashberg ldquoDemand and supply dynamicsfor sequentially released products in internationalmarketsThecase of motion picturesrdquo Marketing Science vol 22 no 3 pp329ndash354 2003

[15] A Elberse and B Anand ldquoThe effectiveness of pre-releaseadvertising for motion pictures an empirical investigationusing a simulatedmarketrdquo Information Economics amp Policy vol19 no 3-4 pp 319ndash343 2007

[16] A M Joshi and D M Hanssens ldquoMovie advertising and thestockmarket valuation of studios a case of great expectationsrdquoScience vol 28 no 2 pp 239ndash250 2009

[17] W D Walls ldquoModeling Movie Success When lsquoNobody KnowsAnythingrsquo Conditional Stable-Distribution Analysis Of FilmReturnsrdquo Journal of Cultural Economics vol 29 no 3 pp 177ndash190 2005

[18] J Eliashberg S K Hui and Z J Zhang ldquoFrom story line tobox office A new approach for green-lighting movie scriptsrdquoManagement Science vol 53 no 6 pp 881ndash893 2007

[19] A Elberse ldquoThe power of stars Do star actors drive the successof moviesrdquo Journal of Marketing vol 71 no 4 pp 102ndash1202007

[20] C Hung ldquoWord of mouth quality classification based oncontextual sentiment lexiconsrdquo Information Processing amp Man-agement vol 53 no 4 pp 751ndash763 2017

[21] S Basuroy S Chatterjee and S Abraham Ravid ldquoHow Criticalare Critical ReviewsThe Box Office Effects of Film Critics StarPower andBudgetsrdquo Journal ofMarketing vol 67 no 4 pp 103ndash117 2003

[22] C C Moul ldquoMeasuring word of mouthrsquos impact on theatricalmovie admissionsrdquo Journal of Economics amp Management Strat-egy vol 16 no 4 pp 859ndash892 2007

[23] P Winoto and T Y Tang ldquoThe role of user mood in movierecommendationsrdquoExpert SystemswithApplications vol 37 no8 pp 6086ndash6092 2010

[24] Y Liu ldquoWord of mouth for movies its dynamics and impact onbox office revenuerdquo Journal of Marketing vol 70 no 3 pp 74ndash89 2006

[25] W D Walls ldquoIncreasing returns to information Evidence fromthe Hong Kong movie marketrdquo Applied Economics Letters vol4 no 5 pp 287ndash290 1997

[26] W Duan B Gu and A B Whinston ldquoThe dynamics of onlineword-of-mouth and product sales - an empirical investigationof the movie industryrdquo Journal of Retailing vol 84 no 2 pp233ndash242 2008

[27] M Bagella and L Becchetti ldquoThe determinants of motion pic-ture box office performance Evidence frommovies produced inItalyrdquo Journal of Cultural Economics vol 23 no 4 pp 237ndash2561999

[28] B R Litman and L S Kohl ldquoPredicting financial successof motion pictures the rsquo80s experiencerdquo Journal of MediaEconomics vol 2 no 2 pp 35ndash50 1989

[29] S Albert ldquoMovie stars and the distribution of financiallysuccessful films in the motion picture industryrdquo Journal ofCultural Economics vol 22 no 4 pp 249ndash270 1998

[30] B R Litman ldquoPredicting success of theatrical movies anempirical studyrdquo The Journal of Popular Culture vol 16 no 4pp 159ndash175 1983

[31] S P Smith and V K Smith ldquoSuccessful movies a preliminaryempirical analysisrdquo Applied Economics vol 18 no 5 pp 501ndash507 1986

[32] J Sedgwick and M Pokorny ldquoMovie stars and the distributionof financially successful films in the motion picture industryrdquoJournal of Cultural Economics vol 23 no 4 pp 319ndash323 1999

[33] A De Vany and W D Walls ldquoUncertainty in the movieindustry does star power reduce the terror of the box officerdquoJournal of Cultural Economics vol 23 no 4 pp 285ndash318 1999

[34] W D Walls ldquoScreen wars star wars and sequelsrdquo EmpiricalEconomics vol 37 no 2 pp 447ndash461 2009

[35] R A Nelson and R Glotfelty ldquoMovie stars and box officerevenues an empirical analysisrdquo Journal of Cultural Economicsvol 36 no 2 pp 141ndash166 2012

[36] J Zhou Y Yuan and P Tu ldquoAnalysis of the collaborationnetwork of Chinese film directors and actorsrdquoComplex Systemsand Complexity Science vol 13 no 3 pp 69ndash75 2016

[37] M Nerlove and K J Arrow ldquoOptimal advertising policy underdynamic conditionsrdquo Economica vol 29 no 114 pp 129ndash1421962

[38] J Feng and B Liu ldquoDynamic impact of online word-of-mouthand advertising on supply chain performancerdquo InternationalJournal of Environmental Research and Public Health vol 15 no1 p 69 2018

[39] A Liu TMazumdar and B Li ldquoCounterfactual decompositionof movie star effects with star selectionrdquo Science vol 61 no 7pp 1704ndash1721 2015

[40] J Forrester ldquoIndustrial dynamics A major breakthrough fordecision makersrdquo Harvard Business Review vol 36 no 4 pp37ndash66 1958

[41] R R P Langroodi andM Amiri ldquoA system dynamics modelingapproach for a multi-level multi-product multi-region supplychain under demand uncertaintyrdquo Expert Systems with Applica-tions vol 51 pp 231ndash244 2016

[42] K Chen and J Yin ldquoInformation competition in productlaunch evidence from the movie industryrdquo Electronic Com-merce Research Applications vol 26 pp 81ndash88 2017

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MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom