Aiken, Game Theory, 2006

7/27/2019 Aiken, Game Theory, 2006

1/19

Journal of Public AffairsJ Publ. Aff 6: 84-101 (2006)Published online inWiley InterScience(www,interscience,wiley,com) DOI: 10,1002/pa,2l6 D I I C O V I N S O H E I H I

A m ixed m otive ap proach to lobbying:applying game theory to analyse theimpact of co-operation and conflicton perceived lobbying successFreya Aitken-Turff and Nigel Jackson*University of Bournemouth, UK This study was motivated by the apparent discrepancy hetween guidance for public

relations best practice using co-operation and collaboration toresolve conflict, and thepotential to use the positive elements of conflictand competition to lobby more effectively.Game theory matrix was applied to nine lobbying campaigns,and used narrative analysisto identify themes of co-operation, conflict, and mixed motive lobbying in the transcripts.The primary research identified that: Conflict, co-operation and mixed-motive lobbying were apparent in all thecase studies. Mixed motive lobbying was unattainable between organizations with diametrically

opposed interests and this may limit its application. A further obstacle to mixed motive strategies is the high level of resources it uses. The numerical game theory matrix used in this study was of limited use, however, the

conceptual framework the theory provided was effective at modelling conflict and co -operation strategies.

Formal co-operative alliances were common in the sample. Smaller coalitionsappeared to be more effective than the larger ones.

Those engaged in high conflict campaigns perceived themselves to be more effective thanthose engaged in lower conflict campaigns, however, this would need to be examined moreexhaustively to establish causality.

Copyright 2006 John Wiley & Sons, Ltd.

Introduction individuals, group s and organizat ions promote^ their interests to Government and politicalThe lobbying industry is fuelled by conflicting ^^^.^.^^ ^^^^^ ^ Q^^xxncn, 1999; Berger, 200 1).ideas, motives, and ideologies as different it js c o m m o n tohear of the pro-and anti-lobbyfurther demonstrating that conflict is acommon feature of lobbying (Bentley et al.,Correspondence to:Nigel Jackson, Bournemouth Uni- |C)C)8 Ja nse y , 2 00 0) . Mo loney (1 99 6a , 20 00 )versity, Weymouth House, Taibot Campus, Fern Barrow, , . . . .Poole BII12 5BB, UK, Sugg ests th at a p lu ra l i s t i c soc i e ty encourages

E mail: njacksonboumemouth,ac,uk co m pe tit io n b e tw e en lob by ing gr ou ps and


2/19

A mixed motive approach to lobbying 85organizations. Public relations literature, how-ever, views conflict very negatively (Vasquez,1996; Plowman et al., 2001) and focuses onconflict resolution as the core purpose of thediscipline (Murphy, 1987), The public relationsprofession is characterized by collaboration(Olasky, 1987; Kearns and West, 1996; Grunig,2000) and its literature prom otes the two-waycommunication model, a process of engagingpublics in mutually beneficial dialogue,described by some scholars as conflict resolu-tion (Murphy, 1987), as best practice by others(Grunig and Hunt, 1984; Kearns and West,1996; Deegan, 2001).

Pressure g roups regularly find them selves indirect conflict with each other (Bentley et al.,1999; Budge etal., 1999), As well as this directconflict, the contact between lobbyists andpolitical decision makers can be seen as aprocess of negotiation, or conflict resolutionQaatinen, 1999), Conflict is not restricted toopposite sides of an issue, indeed many issueshave a range of complex groups trying toinfluence them w^ithout a clear cut pro- andanti-lobby. Groups from the same sector or thesame side of an argument may also generateconflict as they compete with each other toinfluence Govemment,Game theoryGame theory offers both a conceptual frame-work for scrutinizing co-operation and conflict,as well as a mathematical structure to calculateoptimal strategies.' Game theory views situa-tions as 'games', and organizations or indivi-duals acting within those games as 'players'.Each player selects a 'strategy' (makes adecision) and this results in a 'payoff (theoutcomes of the game for all of the players)(Burger, 1963; Davis, 1970; Colman, 1982).Game theory offers a method of modellingconflict and co-operation simultaneously, andhas rarely been applied to lobbying (Fang,2002). Where game theory has been applied to

'A mathematical explanation of these can be found inA ppendix 1,

lobbying, it has been very much limited tomore 'political' aspects. Rasmusen (1993)and Sloop (1997) argued whether the viewsof the electorate was key to lobbying, andChe and Gale (1998) focused on theapplication of game theory to Political A ctionComm ittees for candidates in A merica. Thegame theory paradigm becom es m ost valuablewhen exploring situations where the bestcourse of action for each player will dependon what the other players do (Colman,1982; Nalebuff and Brandenburger, 1996;Kleindl, 1999). Within games, players areinterdependentwhat one player does hasan impact on how another player operates(Davis, 1970).A range of game strategies is available tolobbyists. First, co-ordination games where allthe players' interests are aligned. They arecharacterized by pure co-operation betweenplayers; what one player gains or loses, the co-operating player must also gain or lose. Forexample, if the insurance industry lobbiesprimarily throug h its trade body, th e A ssocia-tion of British Insurers (A BI), if the ABI fails tolobby effectively for its mem bers ' interests, allthe members fail. Second, competitive gamesare characterized by players' diametricallyopposed interests (Davis, 1970) where what-ever one player gains another player must lose.In such 'zero-sum' games a player will bemotivated to reduce h is/her op pon ent's payoffin order to achieve the highest payoff for him/

herself. The pro- and anti-abortion lobbies aregood examples ofa zero-sum game. If the anti-abortion lobby were to achieve its abolition inth e UK, the pro-abortion lobby would lose andvice-versa. Third, mixed strategy games arewhere the interests of players are neitherstrictly opposed nor strictly congruent (Davis,1970; Colman, 1982; Murphy, 1991), Playersseek a win/win outcomethe outcome thatbenefits all players to the maximum it canwithout hurting another player. This mixedstrategy is the most common (as even in thesimplistic examples above, there is potentialfor organizations to have subtle differences,therefore, not aligning or opposing theirinterests so starkly).


3/19

86 Freya Aitken-Turff an d Niget JacksonA vast proportion of existing game theoryresearch has focused on computer basedlaboratory experiments that analyse partici-pants' favoured strategies (Burger, 1963; Davis,1970; Colman, 1982; Amaldos and Jain, 2002;Kaluski, 2002). This body of research mayreinforce the notion that game theory does notapply to the complex realities of social situa-tions (Harrison, 1995). Game theorists arguethat unless game theory is applied to 'real life' itwill remain sterile andonly of mathematicalvalue (Davis, 1970; Colman, 1982; Nalebuff andBrandenberger, 1996). This article examinesgame theory's potential to analyse lobbying

campaigns.Mixed motive public relationsIn response to criticisms of the two-waysymmetrical m odel of public relations. Murphy(1987, 1989, 1991) combined the principles ofgame theory with the co ncep ts of symmetry toconstruct the mixed motive model of publicrelations. Here an organization tries tomeet itsow^n objectives whilst at the same timeattempting to help othe rs achieve theirs. Mixedmotives recognize that it is possible to be bothco-operative and competitive in the samecampaign Qaatinen, 1999; Fang, 2002). Grunig(2001) endorsed the m ixed motive approach asone that could describe symm etry in the way heoriginally intended. Two-way communicationcan only be realized if its primary motivation isto find the win/win strategy between anorganization and its stakeholders (Plowmanetal., 200]).

LobbyingLobbyists, whether they are from commercialorganization, trade bodies or pressure groups,aim tofirst nform, and then persuade, politicaldecision makers of their causes (Hollings-worth, 1991; Souza, 1998; Miller, 2000). Inter-est groups are a key factor in policydevelopment (Zeigler and Baer, 1969; Smith,1993), and the wide range of interests whichengage in lobbying activities makes studyingthem complicated (Baggott, 1994; John, 2002).

Lobbying is the process bywhich economicand non-commercial interests are represe nted,and can have their voice heard within thepolicy making community (Graziono, 2001).Indeed, Moloney (2000) suggests that lobbyingis the means by which smaller, less overtlypowerful sections of society can redress thepower balance.Throughout this article the terms 'organiza-tion' and 'gro up' are used to describe any entityinvolved in lobbying. Groups aim to achievetheir objectives using three channels of influ-ence (Baggott, 1994):(1) Influence over those who m ake policy,(2) Influence over the political agenda,(3) Influence over the attitudes ofthe public.We are concerned with how organizations canuse conflict and co-operation to influence thefirst two of Baggott's channels as our focus is onlobbying.ConflictConflict occurs when people identify adiver-gence of interests and believe that their ownobjectives cannot be achieved simultaneouslywith those of the othe r party/parties (Deutsch,1973; Lulofs and Cahn, 2000). Business litera-ture suggests conflict is a waste of resources(D'Aveni andGunther, 1995). However, otherscholars argue that conflict makes individualsmore creative and generates higher qualityproblem solving (Plowman, 1995; Lulofs andCahn, 2000). In the lobbying context, conflictoccurs when groups perceive that their inter-ests are different to those ofthe govem men t, oranother group attempting to influence govem-ment. In conflict situations, pe ople can becomeincreasingly creative and demonstrate higherdegrees offlexibilitywithin the ir own organiza-tions (Lulofs and Cahn, 2000). In such situa-tions conflict can be beneficial to groupperformance (Van Drew andVan De Vliert,1997; Wong et at., 1999). However, otherauthors suggest that conflict disrupts theexchange of information and can destabilizethe commitment needed to implement deci-sions effectively (Amason and Schweiger,


4/19

A mixed motive approach to lobbying 87t997 ). The existence of a perceived differenceof interests is one ofthe key factors that shapesa lobbyists chosen strategy.Whitst one approach views lobbying asinformation flows (Austen-Smith, 1995), wesuggest it is more likely to be about winning,and being see to w in. With lobbying focusingon influencing decisions, a high conflict zerosum strategy may prove more effective atgenerating favourable policy outcomes. Themixed motive approach uses a combination ofco-operation and co nstructive conflict to reacha mutually satisfactory outcomeeither awin -w in or a no deal. Some suggest this is themost effective form of lobbying as it balancesthe pow er of the organization w ith the p owerof its publics (Murphy, 1987; Plowman, 1998;Plowman et al, 2001). These differing strate-gies cannot be analysed in terms of effective-ness unless a method of establishing lobbyingeffectiveness can be realized.Formal co-operationalliancesand coalitionsCo-operation theory attempts toexplain howand why individuals and groups use co-opera-tion to achieve their goals without the involve-ment of an external authority (Axelrod, 1984).The theory focuses on long-term relationshipsas it is only after an alliance, or a period of co-operation has matured, that co-operationbecomes the preferred strategy. Co-operationtheory was ex tended to develop th e Tit for Tatmodel. This proposes retaliating in kind to theopponent against uncooperative behaviour,but quickly forgiving the opponent if theystarted to behave in a co-operative fashion.Murphy and Dee (1992) found that th e Tit forTat model was apparent in relationshipsbetween companies and activist groups.Business literature focuses on the assessmentof alliances and coalitions. An alliance is theumbrella term for a variety of cooperativerelationships (Faulkner and DeRond, 2000).Game theory allows for the costs and benefits ofalliance or coalition membership to be repli-cated. The framework shows that coalitionmem bership does not gua rantee higher payoffs

(Burger, 1963; Kaluski, 2002). Mathematicallyin a game that allows coalitions, the payoff forany player is calculated on the number ofcoalition members. This links to the sizeprinciple (Colman, 1982), if a player hasenough weight towin the payoff alone, theywill not seek coalition members. Each game hasa limited payoffa maximum am ount that th eplayers can win. In coalition games, the payoffmay increase as the n umber of players increasebut only to a limited point. No incentives existfor forming coalitions larger than the minimalwinning size (Davis, 1970; Colman, 1982;Nalebuff and Brandenburger, 1996).Lobbyists are also interested in coalitions,indeed Graziono (2001) suggests that lobbyingis nearly always conducted through coalitions,rather than individually. Whilst Olsen (1965)suggests that pressure group might, by theirvery nature, be inclusive, the more likelyexplanation for coalitions is that they poten-tially give the individual mem ber m ore politicalclout (Moloney, 2000; Graziono, 2001). How-ever, whilst a lobbying coalition might beconsidered the norm, game theory raisesquestions on the optimum size of a coalition.Keeping the coalition to the minimal winningsize means that the payoff is divided amongfewer players. The size principle may motivatelobbyists to restrict themembership of theircoalitions (such as trade associations) in orderto achieve maximum payoffs. Murray andMahon (1993) developed the alliance lifespanto describe the direct correlation between thecomm itment of resources and the commitmentof time that a formal alliance uses. The longer analliance lasts, the more resources it uses.However, if the alliance is ended too quickly,the time and resources compared to the outputofthe alliance is in the negative. This highlightsthe need for coalitions to be analysed andunderstood in greater detail in order to achievethe optimal strategy for each player or organi-zation.

fudging lobbying effectivenessEstablishing the effectiveness of lobbyingactivity is difficult; how do you disaggregate


5/19

88 Freya Aitken-Turff and Niget Jacksonthe role of lobbying in how a decision is made(Moloney, 2000)? This problem is exacerbatedif there are groups active on multiple sides of anissue because there are multiple o pportunitiesfor a lobbyist to claim they were instrumental inmaking effective changes in legislation (Jordan,1991; Bentley et al, 1999). The majority oflobbying activity is carried out in private,making influence difficult to judge (Moloney,1997; McNair, 199 9). John (200 2) suggests thatlobbying effectiveness depends on both exter-nal, such as the political environment, andinternal factors including th e skills of lobbyists.Moloney (1996b) adds that 'hired' commerciallobbyists are also constrained by the institu-tional factors placed by their clients. John(2002) suggests that it is the external factorswhich have the greatest impact on lobbyingeffectiveness, so that it iswith highly technical,non-political issues where lobbyists are morelikely to be successful.

Overall the most effective form of evaluationcurrently available to lobbyists is whether thelobbying party achieved what it set out toachieve (Hendrix, 1988). As the decisionmaking process can be opaque (McNair,1999), it would be impossible to study eachaspec t of interest group activity to demonstratewh at had the m ost effect. An alternative optionis to ask interest group s for their p erception s oftheir own effectiveness as a great deal ofrelevant data can be gathered in this way(Whitely and Winyard, 1987; Grant, 2000).MethodologyThis article seeks to answer four questions:(1) To what extent are conflict and co-opera-tion strategies used in lobbying campaigns?(2) What is the impact of conflict and co-operation on perceived lobbying success?(3) How accurate is game theory at predictinga player's conflict style in lobbying cam-paigns?(4) Are mixed motive strategies used in lobby-ing campaigns?

The sample was selected from two samplingframes:

(1) The E-politix forum of 195 members withcontact details for staff involved in politicallobbying (www.epolitix.com). Six of therespondents in the sample came from thissampling frame.(2) Issues that have dominated the UK policyagenda in the previous 2 years included foxhunting, drug reclassification, airportexpansion. An Intemet search was thencarried out on these subjects and threeorganizations agreed to participate fromthis sampling frame.These sample frames were used as theorganizations that had paid the E-politix sub-scription fee were likely to have been politi-cally active in the last 2 years a suitable timeperiod for participants to be able to rememberwhat happened during the campaign (Yin,1989; Rose, 199 1). Similarly, the organizationsthat were found through a Internet search we realso likely to have been active since the issuesthey focused on had recently been debated inParliament. In addition to this general selec-tion, the organizations we specifically con-tacted were chosen because they had a 'live'issue that had either before Parliamentrecently, or was currently being discussedwithin the policy making environment. More-over, a range of organizations, includingcharities, pressure groups, and commercialcompanies were selected. As a consequencethe issues chosen varied from high-profile ones

at the heart of public debate through to those ofspecialist interest. Therefore, the individualselected organizations and issues were chosenbecause collectively they added up to a widecross-section.Table 1 outlines the numerical values givento the samples responses. A conflict interde-pendence style on a scale of -t-5 (Promotive)through to 5 (Contrient) w as adapted fromPlowman (1995) and Murphy (1987). Asconflict literature views promotive conflict assomething positive that should be fostered,promotive conflict is at the high scoringen d of the scale. Being highly promotive isequivalent to being co-operative. Contrientbehaviour (viewed negatively in public


6/19

A mixed motive approa ch to lobbyingTable 1. Framework for game theory analysis

Promotive Contrient

89

IndependentPromotiveContrientIndependent

5 (5) W in/win/no deal.Govemment decides winners3 ( -5 )2(0)

- 5 ( 3 )5 (5) Players receive samepayoffs. Govemment decides- 4 ( 0 )

negativewinner/s0(2)

0 ( - 4 )0 (0) Govemmentdecides winner/s

relations literature) receives negative payoffsand is scored at the lower end of the scale(Deutsch, 1973). Players scoring nearer to zeroare viewed as having an indepen dent style. Thegame theory matrix in Table 1 is a standardDavis (1970) payoff matrix for two playergames. The m atrix is for the organization beinganalysed and their payoffs are represented inthe columns. Where the number is positive, theplayer wins points (a greater chance ofsuccess), where the numbers are negative,the player con cedes points (and is more likelyto be unsuccessful). The numbers in bracketsare what the opponent will win or lose if thatstrategy is played.The winning strategy is the one that corre-sponds to the strategy played by the opp one ntwhich yields the highest payoff. For example, ifthe opposition played a contrient strategy, theparticipant could select from the followingavailable strategies: Promotive: 3 (- 5 ) Contrient: - 5 ( -5 ). Players receive the samenegative playoffs. Government decides win-

ner Independen t: 0 (-^4)The optimal strategy, in the above example,is promotive as the payoff for the player ishighest (3 points for the player and - 5 for theopponent).

FindingsThe type of games that the participants hadbeen engaged in were identified from theinterview data. Table 2 below shows theorganization, gives a summary ofthe campaign

case study, and the type of game their campaignwas interpreted as. It iswo rth noting that eachof our lobbying sample was looking for a 'bigticket' change, rather than small incrementalchange in policy.However, it also became apparent thatparticipants were often involved in additionalrelationships that could be categorized by asecondary gamewithin the same campaign. Forexamp le, on the issue of fox hunting the P7wasinvolved in a zero-sum game with the pro-hunting lobby, and, at the same time areinvolved in a game of pure co-operation withP8. In light of this participan ts we re categorizedby primary and secondary games show^n inTable 3:

The occurrence of secondary games is not afeature of the literature. Traditional gametheorists view the two games as separatestructures and ignore that they interlink (Nale-buff and Brandenburger, 1996). However, asthe two games were features of the samecampaign, it was more logical in this study tocategorize them as primary and secondary.Phases of gamesThe participants that were engaged in second-ary games of pure co-operation reported havingto negotiate a great deal before entering in tothat game/alliance. This suggests that beforeorganizations enter in to a pure co-operationgame, they m ust play a mixed motive game toestablish the joint position/strategy for thepure co-operation game. If this is the case thenanalysing lobbying in game terms players maygo through each ofth e three games in turn. Forexample, P7 and P8 had to play a mixed m otive


7/19

90 Freya Aitken-Turff and Nigel JacksonT a b l e 2. Primary game theory strategy of sampleParticipant Nature of organizationcode

Campaign summary Type of game

PIP2

P3

Campaigning organization focused onhousing needsMultinational financial services company

Registered charity focused on socialwelfareUmbrella body that representschildren's NGOs

To make the right to buy system more Mixedsustainable motiveSandier pensions review price caps. MixedFocused on setting the price cap at a motivesustainable levelGambling bill. Focused on limiting the Zero sumliberalization ofgambling reform in the UKAnti-social behaviou r bill. Focused on Mixedremoving elements of the Bill that wo uld motiverestrict the freedom of young people.Sexual Offences Bill. Focu sed on limitinglegislation so that young people are p rotecte dbut retain the ir freedom of consen tP5

P6P7

P8P9

Large leisure intere sts PLCNetwork organization focused on drugpreventionMem ber funded cam paigningorganization advocating the abolitionof huntingNational charity focused on animalwelfareInternational airline

Licensing laws. Focused on liberalizing UKlicensing lawsCannabis reclassification. Focused onopposing the reclassification of cannabisFox hunting. Focused on the abolitionof fox huntingFox hunting. Focused on the abolitionof fox hun ting.Heathrow expansion. Focused onpromoting the development ofan additional runw ay

MixedmotiveZero sumZero sum

Zero sumMixedmotive

*P4 was involved in two campaign s with very different conflict and co-operation styles. Rather than select on e or theother, data were collected on both case studies.

game before engaging in a pure co-operationgame in order to comp ete against the p ro-huntlobby in a zero-sum game. In previous literaturegames vvere viewed in isolation and not as

interdependent (Nalebuff and Brandenburger,1996). If the construct could be adapted toreflect the inter-linked games that a player willengage in, this could offer a method of viewingTable 3. Secondary game theory strategy of sampleParticipatin g Primary gam eorganization Secondary game summary Secondary gamecategorizationPIP2P3P4AP4BP5P6P7P8P9

Mixed motiveMixed motiveZero sumMixed motiveMixed motiveZero sumMixed motiveZero sumZero sumMixed motive

Organization remained independentExchanges of information with competitors andopposing groupsIn a formal coalition with the Methodist ChurchIn a formal coalition with 11 oth er organ izationsIn a zero-sum game w ithin the coalitionIn a formal coalition with 40 -f- other organizationsand individualsIn formal coalition with o ther leisure industry com paniesIn formal coalition with tw o other animal welfare groupsIn formal coalition with t wo o ther animal welfare g roupsIn formal coalition w^ith other airlines

N/AMixed motivePure co-operationPure co-operationZero sumPure co-operationPure co-operationPure co-operationPure co-operationPure co-operation


8/19

A mixed motive approach to tobbying 91the implications of strategies earlier in thegame.The use of game theorymathematics to predictlobbying strategiesThe authors categorized the participants' gamestrategies as either promotive, contrient orindependent based on their reported lobbyingstyle. Once the games had been categorized,the game theory m atrix was used to predict thelobbying outcomes. The payoffs range from -5to 5 with 0being neutral the payoffs repre-sent thedegree that theparticipants' achievedtheir objectives and was calculated from theirself-recorded score out of ten for achievingtheir aims. Thepredictions made by thegametheory matrix are show^n in Table 4.The game theory matrix shown in Table 4 didnot predict the behaviours of the sample toprovide any significant degree of predictivevalidity. One ofthe difficulties of applying gametheory to the research narratives is the com-plexity of coding the data (Colman, 1982;Murphy, 1987). In this study, the lobbyingstrategies identified had to be greatly simplifiedin order to make the calculations. Inorder tocalculate numerical values for every possiblestrategy that each player could possibly takewould need an infinite payoff matrix (Davis,1970; Colman, 1982). It should be noted,however, that ifparticipants had access to thepayoff matrix during campaigns the matrix may

offer viable strategies that theparticipant maynot have previously considered (Murphy, 1987,1991; Harrison, 1995).Although the mathematical constructs ofgame theory did not prove high in predictivevalidity in this study, the theory still prov ides auseful construct todescribe behaviours. Thelanguage of games, winning, and losing wascommon amongst the participants, for exam-ple: 'In this game it's no good coming second.'(P4). This is also a feature of lobbying literature(Graziono, 2001; John, 2002). This maydemonstrate thevalue of using game theoryas a way of modelling lobbying campaigns. Iflobbying professionals are already thinking oftheir work in game terms, the theorymight offer a method of viewing strategiesthat professionals would easily understand(Harrison, 1995).Reported conflict style andthe tit for tat modelThe participants engaged in campaigns whereconflict was prominent all described a situationwh ere their oppone nts sought toattack them.For example, the P3 stated:

'Their [the opposition's] mechanism is to tryand discredit us at the moment becausethey're very scared'.All respondents wh o rep orted these kinds oftactics (apart from P4) had responded withindependent tactics in their campaigns. The Tit

Table 4. Game theory prediction

Organization

PIP2P3 AP 3 BP4P5P6P7P8P9

Optimal game theory strategy

Promotive (Govemment decides)PromotivePromotive (Government decides)Promotive (Govemment decides)Contrient (Govemment decides)Contrient (Govemment decides)Contrient (Govemment decides)Contrient (Govemment decides)ContrientPromotive

Payoff

5355- 5- 5- 5- 5- 52

Actual strategy

IndependentIndependentPromotiveContrientIndependentIndependentPromotiveContrientContrientPromotive

Accurate gametheoiy prediction

NoNoYesNoNoNoNoYesYesYes


9/19

92 Freya Aitken-Turff and Niget Jac ksonfor Tat model (Axelrod, 1984) pred icts that theplayers would respond similarly. The data didnot reflect this pattern, although it could beargued that an independent strategy could bejust as disruptive to the opposing groups.Contrient behaviour uses resources and so bynot retaliating, the opponent's resources arewastedproviding they do not discredit orharm th e reputation ofth e organization. Therewere noexamples of the 'forgiveness' exem-plified in the Tit for Tat model.

Only one of the participants reported usingdestructive conflict strategies in their cam-paign, and even then it was in response to anopponent's contrient style. This appears tosupport the Tit for Tat model (Axelrod, 1984).However, the other participants that reportedcontrient strategies from their opponentsreportedly responded with avoidance strate-gies that is ignoring the opposition, ending ornot entering in to dialogue with them. Most ofthe sample reported a constructive conflictstyle. This may reflect the conflict style of th esample, or that they might not admit tobehaving in a m ore destructive way.The benejits of co-operationParticipants cited three key benefits to formingalliances and building cooperative relation-ships with groups with similar views as theirown. Firstly, it increased the amount of staffresources available to them. Secondly, itincreased moral support and a sense of notbeing alone. Thirdly, it increased each organi-zation's credibility, as they are part of a muchwider body of opinion.The participants who raised the moralsupport issue were all engaged in zero sumgames, therefore high conflict campaigns (P3,P4, P5, P7, P8). This may reflect the importanceof being part of a wider group if engaged indirect conflict, or it may reflect the nature oftheorganizations that reported itorganizationswith smaller lobbying functions (often a singleperson). A person working alone may value thesupport of others working towards a similargoal than a person in a larger lobbyingdepartment.

A number of drawbacks of forming allianceswere also cited. All participants felt thatforming co-operative relationships and nego-tiating agreed positions within those relation-ships took a great deal of time. This may reflectthe alliance lifecycle deve loped by Murray andMahon (1993), the more time and resourcesspent in building an alliance, the more formalthat alliance becomes. This may suggest thatmixed motive lobbying takes too m uch time fororganizations to pu t it in to practice, P4 and P5(the participants that reported a great deal ofexperience in forming coalitions) believed thatbeing a member of a coalition can make it hardto be dynamic and responsive, P4 likened theexperience to 'being constipated' by thenum ber of coalition members.Formal co-operationInterestingly P8, when questioned about any-thing it would change in hindsight, believedthat a written agreem ent for its coalition w ithP7 and one other organization (not involved inthis study) would make the alliance moreefficient. The respondent suggested that suchan agreement would help in:

'setting the lines and the bou ndaries that youwon't cr os s,, , that's not to say that nothaving this [contract] had a major effect onour campaign but probably just to have acontract would assist working through anydifficulties that might come up'.This contract would formalize the win-winagreement that the alliance members hadagreed up on. If this was the case, the alliancewould progress along both Lorange and Roos'(1993) alliance continuum and Murray andMahon's (1993) alliance life-span to a highdegree of interdependence. This increase ininterdependence may lead to more opportu-nities for conflict (Deutsch, 1973),

Mixed motive lobbyingand resourcesThe three businesses in the sample (P2, P6 andP9) described being involved in mixed motive


10/19

A mixed motive approach to tobbying 93strategies with a variety of com peting interestgroups. This may reflect tha t groups with largerfinancial resources have more capacity toengage with other interest groups. It may alsosuggest that these organizations subscribemore to the model of mixed motive publicrelations (Murphy, 1987, 1991; Grunig, 2001;Plowman et al., 2001). In contrast, P5 (theparticipant with the fewest resources andmembers of staff) struggled to achieve two-way symmetrical communication, though notthrough unwillingness or believing it was oflittle value:

'If there we re more of us here then we w ouldfeel more able [to engage in dialogue withgroups w^ith opposing ideologies] but wehave to be pretty selective where w e put o urhours in'. (P5)The other very small organization in thesample (P4) did report engaging in more two-way symmetrical relationships than the P5, bu tthe na ture ofthe organization (an alliance madeup of children's NGOs) means that P4 can

access a variety of organizations and createdialogue more readily than P5. This maysuggest that the two-way symmetric model ofpublic relations and the mixed motive modelare difficult for organization w ith less resourcesto utilize (Karlberg, 1996).Mixed motive lobbyingParticipants reported that entering into dialo-gue with groups with diametrically opposedinterests was futile. This finding might beexplained by the fact that our sample were allinvolved in finite games with clear outcomes.There needed to be some common ground,which suggests mixed motive lobbying cam-paigns would be impossible if both partieswere not committed to finding a win-winoutcome. Groups did not seek to engage theirdirect opponents but did form relationshipswith other organizations to find win-winsolutions. For exam ple:

'I think that there was middle ground andthat's pretty much what w e got'. (P9)

All the participants reported taking part inmixed motive lobbying, and noted that con-sidering the opposition's arguments could bevery positive. For example: 'Your best line ofdefence or attack in lobbying is to have takenon board and understand and maybe evencompromise towards the people who areagainst you' (P6).Considering the views of other playersreflects the view that persuasive argumentsbecome more effective when opposing viewsare considered (Ury, 1991; Perloff, 1993;Mitchie, 1998). However, the motivation forworking with or entering in to mixed motivegames was not consistently reported as findingthe common ground. The members of thesample that did report engaging with theirdirect opponents (P5, P2, P4, PI ) all describedpart ofthe motivation as 'knowing what they'reup to'. This may suppor t R owell's (2002) claimthat organizations only engage in dialogue w iththe opposition in order to create strongercounter arguments against their rival interestgroups. However, the opposing organizationswould also strengthen their counter argumentsby participating in the dialogue, and so bothparties become stronger from the interaction.Game theory can calculate the optimumcoalition size but not, however, withoutextremely complex calculations or perfectinformation about the different coalition mem-bers (Nalebuff and Brandenburger, 1996). Iforganizations cannot calculate their optimumcoalition size, it reduces the decision to ente r into a coalition back to gut feeling, personalpreference and previous experience. Gametheory does not necessarily, therefore, explainhow many members there should be in acoalition before th e interests of its mem bers arediluted.

The impact of conflict andco-operation on perceivedlobbying successTable 5 compares the participants' degree ofconflict and co-operation, with their perceivedlevels of success. The sample appeared to showa link between levels of conflict and perceived


11/19

94 Freya Aitken-Turff and Niget JacksonTable 5. The degree of conflict and co-operation compared with perceived success levelOrganization

PIP2P3P4AP4 BP5P6P7P8P9

Dominant co-operation/conflictstyle with oppositionNeutralNeutralHigh contlict. Strong opp ositionConflict with Govemment proposals.Small oppos itionHigh conflict, opposition withinthe coalitionHigh conflict. Strong oppositionLittle conflict. Moderate oppositionHigh conflict. Strong oppositionHigh conflict. Strong oppositionHigh conflict, (Strong opposition

Dominant conflict/co-operationstyle within same sectorIndependent, Informal co-operativerelationshipsIndependent, Informal co-operativerelationshipsFormal coalition (high co-operation)I'ormal coalition (high co-operation)Informal coalition (co-operative)l'ormal coalition (high co-operation)Formal coalition (high co-operation)Formal coalition (high co-operation)I'ormal coalition (high co-operation)Formal coalition (high co-operation)

Perceived lobbyingsuccess

8880.1866976

levels of success. The participants involved inthe zero-sum games, particularly the partici-pant who was involved in a zero-sum secondarygame (P4), and therefore w ere in high conflictcampaigns, appeared to view their successesmore positively than those engaged in mixedmotive games. Those involved in secondarygames of pure co-operation, who were engagedin zero-sum primary games, also appeared moresatisfied with payoffs from the co-operationgames. This suggests that higher levels ofconflict can make any concessions that alobbyist wins from political decision makersmore satisfying. The explanation for this maybe that zero-sum games are most likely whenthe outcome is particularly important to thatorganization.The portion ofthe sample that were involvedin pure co-operation within mixed motivegames reported more concerns about theamount of time the pure co-operation took toco-ordinate (P4, P5). This may suggest thatorganizations involved in direct conflict aremore prepared to invest time and resources insecondary games of pure co-operation thanorganizations without that direct level ofconflict. This may also support the positiveelements of conflict cited earlier (Van Drewand Van De Vliert, 1997; Green, 1999; Wong et

Both PI and P2 approached their campaignswith a predominantly independent strategy,choosing informal co-operation with a range ofgroups. Both participants shared their view^swith groups from the same sector and frompotential opponents. Interestingly, both orga-nizations repo rted a high degree of success. P7and P8 were part of a small formal alliance,which was modelled as pure co-operation ingame theory terms. However, in a pure co-operation game, payoffs for both players aresymmetrical. In terms of perceived success, P7rated its campaign as nine out of ten, and P8 asseven out often. This suggests that the lobbyingpayoffs in this game are not symmetrical. It mayreflect tha t the organizations are engaged in amixed motive game, rather than a purecooperation game. This would account forhigher payoffs for one ofthe players. It may alsoreflect a limitation of comparing perceivedsuccess as different participants may havedifferent perceptions of their degree of suc-cess. The G overnment's position and personalrelationships were also identified as factors thathad an influence on lobbying effectiveness.Formal evaluation w as rare in the sample. Untila more valid or scientific method has beendeveloped, perceived success levels remainone of the only measurements available to


12/19

A mixed motive approach to tobbying 95ConclusionsConflict and co-operation were common ele-men ts in all ofthe lobbying campaigns analysedin this study. Participants reported limitedexperiences of destructive conflict, even inresponse to their opponent's contrient strate-gies. This counters the predictions made by th eTit for Tat m odel. This may call the validity ofthe Tit for Tat model in to question, or it mayreflect the limitation of self reports as theparticipants may not have wanted to admit tonegative strategies. We argue that the Tit for Tatmodel is not the best explanation of thelobbying process. Both formal and informalco-operation were reported by all the partici-pants. Alliances were comm on and th e samplehad all had experience of this type of co-operative relationship. Trust had to developbetween the participating organizations andtheir publics. This reinforces the theme fromthe literature that co-operative relationshipstake time to develop, and could strengthen th ecase for long-term relationships in publicrelations theory.

Participants that were involved in highconflict situations w^ith a direct (and oftenhighly contrient) opposition reported slightlyhigher levels of perceived success. It maysuggest that higher levels of conflict lead togreater determination to succeed. This wouldneed to be tested using a more scientificmethod to establish a link or causality.The participants involved in high conflictcampaigns did not report concerns about thetime and resou rces used in lobbying. This couldimply that effectiveness is linked to the timeand resources rather than conflict. The conflictprovides the motivation to spend more timeand resources lobbying the cause, which inturn could make campaigns more effective.Participants involved in large formal co-opera-tive alliances reported that this limited theireffectiveness as they could not b e dynamic andresponsive. This may suggest that flexibilityand responsiveness are determiners in lobby-ing effectiveness. The organizations that wereinvolved in smaller alliances believed that theco-operative relationship made their lobbying

campaign more effective. This indicates that co-operation and alliance formation can impact onperceived success, however, the alliance needsto be small in order to be effective.This study attempted to use game theory topredict a p layer's success based on their chosenconflict strategy. The mathematical methodfailed. This may reflect th e problem of reducingcomp lex lobbying games down to a simplistictwo player game. However, the descriptiveaspects of the theory (as opposed to themathematical aspects) were identifiablethroughout the research data and provide auseful set of terms to analyse the interv iew datawith. The language of games was commonamong the sample. This may endorse the use ofgame theory in planning lobbying strategies,even if the mathematical formula was low inpredictive validity. Organizations involved insecondary games of pure co-operation hadpreviously engaged in a mixed motive gamein order to find the win-win zone, whichbecame the organization's lobbying message.Game theory could not, however, account forpersonal relationships. The entire sampleplaced importance on these relationships andthis may restrict game theory's use in predict-ing success.

Participants engaged in games of pure co-operation had already played a mixed motivegame in order to settle on a win-win argument.This phenomenon had not been identified inany of the previous scholarship reviewed forthis article.Participants did rep ort mixed motive strate-gies in their lobbying campaigns. However,interaction with groups that held directlyopposing views was rare. This may reflect alimitation of the mixed motive model, andreinforce that an organization mayfindsome ofits public morally abhorrent making two-waycommunication difficult, if not im possible. Thesample believed that collaborating with groupswith directly op posing interests was pointless.This brings the universal application of mixedmotive public relations into question. Themixed motive method may be effective forcreating win-win or no deal situations withsome of an organization's pub lics, however, it


13/19

96 Freya Aitken-Turff and Niget Jacksonappears unlikely from the data gathered in thisstudy that mixed m otive pub lic relations can beapplied to all of an organization's publics. Thesample also identified that mixed motivetechniques of negotiation used resources. Thismay limit the effectiveness of the method as agroup would need to invest in order to reap thereported benefits. This implies that the mixedmotive model would not be the most effectivelobbying strategy for an organization withfewer resources.

We suggest that that the findings of thisarticle imply that lobbyists could plan theircampaigns a different, and potentially moreproductive way. Our data suggest that thelanguage of winning and losing is alreadycommon in the experience of lobbyists, andin the lobbying literature. This reinforces thesuggestion that using game theory constructsmay add value to the lobbying planningprocess. In Table 6 we outline a Payoff Matrixmodel that offers lobbyists a framework forjudging the appropriate strategy they shouldtake.To utilize a Payoff Matrix lobbyists need toassess their wider environment, especiallywhat potential opponents may do . We identifyfive possible (and not mutually exclusive)strategies which lobbyists might employ based

on their research of the situation. Whilstorganizations may or may not b e able to affordto conduct detailed research, we suggest thatthe Payoff Matrix model encourages them toask appropriate questions to help them selectthe appropriate lobbying strategy. Answeringthese questions may not only just help anorganization decide the best appro ach for itself,but also what might harm opponents. Forexample, publicizing that an oppo nen t is usinga contrient approach in order to damage theircredibility. Whilst this model is limited by theaccuracy an organization has on potentialopponents (and allies), it does provide astructure by which lobbyists can use GameTheory constructs at the beginning of acampaign.

This study was motivated by the apparentdiscrepancy between guidance for publicrelations best practice using conflict resolutionmethods, and the potential to use the positiveelements of conflict and competition to lobbymore effectively. Co-operative, conflict, andmixed motive strategies were apparent, how-ever, the research could not identify whichstrategy was more effective. This article appliedgame theory to formulate and analyse coopera-tion and conflict in lobbying campaigns.Although the mathematical matrix of game

Table 6. Payoff matrix modelPossible strategy Questions to askOutcomePotential for conflictPotential for co-operation

Mixed MotiveTime/Resources

Existing/predicted behaviourof opponents

Is there a clear win/lose (zero sum) outcome?Is another interest group asking (or likely to ask) Government for the opposite to theorganization 's goals?Is another organization with diametrically opposed interests likely to be lobbying?Can the organization achieve its objectives alone?Is another organization likely to make the same demands of Govemment?What size of coalition is desirable/acceptable to the organization?Would the organization's message be amplified in a coalition, or diluted?How willing/able is the organization to compromise?Is there potential to work with oi^anizations that have opposing views?What stage of policy making is the campaign at?What resources does the organization have to comm it to collaboration?Is the organization already engaged in formal collaboration?Does the Tit for Tat model apply to opponents?Are opponents conducting a zero-sum strategy?Could the organization get an opp onen t to waste time and resources by being inconflict with it?


14/19

A mixed motive appr oach to lobbying 97theory failed to offer the strategies of theorganization, its constructs provide w^ays ofassessing th e values of lobbying strategies.Biographical notesFreya Aitken-Turff is a Policy Analyst forHBOS pic .

Nigel Jackson is aSenior Lecturer in PublicRelations, University of Bo urnem outh .ReferencesAmaldos W, Jain S. 2002. David vs Goliath: an

analysis of asym metric mixed-strategy games andexperimental evidence Management Science48(8): 9 7 2 - 9 9 1 .

Amason AC, Schweiger DM. 1997. Conflict as anegative force. In Conflict. From. Theory To Action,Lulofs, Cahn (eds). Sage: London, Chapter 7.

Austen-Smith D. 199 5. Cam paign Con tributions andAccess. Am erican Political Science Rev iew89(93): 5 6 6 - 5 8 1 .

Axelrod R. 1984. The Evolution of Cooperation.Basic Books: New York.

Baggott R. 1994. Pressure G roups: A Question ofInterest. Sheffield Hallam University: Sheffield.Bentley R, Dobson A, Grant M, Roberts D. 1999.British Politics in Focus. Causeway Press Ltd:Ormskirk.

Berger BK. 2001. Private issues and public policy:locating the corporate agenda in agenda-settingtheory. Journal of Public Relations Research13(2): 91-126.

Budge I, Klingeman H-D, Volkins A, BaraJ. 1999.Mapping Policy Preferences Estimates forParties, Electors, and Governments, 1945-1998. Oxford University Press: Oxford.

Burger E. 1963. An introduction to c urrent mathe-matical concepts of the theory of games withsignificant applications. Introduction to theTheory of Games. Translated by Freund JE.Prentice Hall: Englewood Cliffs, NJ.

Che Y-K, gale 1.1998. Caps on p olitical lobbying, neAmerican Economic Review 88(3): 643-651 .

Colman A. 1982. Game Theory and ExperimentalGames. The Study of Strategic Interaction.Oxford/Pergamon Press: New York/Paris.

D'Aveni RA, Gunther R. 1995. Hyper CompetitiveRivalries. Competing in a Highly DynamicEnvironment Free Press: New York.

Davis A, 1970. Game Theory. A NontechnicalIntroduction Revised Edition. Basic Books Inc:New York.

Deegan D. 2001. Managing Activism: A Guide toDealing with Activists and Pressure Groups.Kogan Page: London.

Deutsch M. 1973. The Resolution of Conflict YaleUniversity Press: New Haven, CT.

Dozier DM, Grunig LA, Grunig JE. 19 95. Manager'sGuide to Excellence in Public Relations andCommunication Management Lawrence Elr-baum: Mahwah, NJ.

Fang H. 2002 Lottery versus all-pay auctionmod els of lobbying. Public Choice 112 : 351 -3 71 .

Faulkner D, De Rond M. 2000. Co-operativeStrategy: Economic, Business, and Organisa-tional Issues. Oxford University Press: O xford.

Grant W. 2000. Pressure Groups & British Politics.Macmillan: Basingstoke.

Graziono L. 2001. Lobbying, Pluralism and Democ-racy. Palgrave: Basingstoke.

Green A. 1999. Creativity in Public Relations. IPRKogan Page: London.

Grunig JE, Hunt T. 1984. Managing Public Rela-tions. Holt, Rinehart and Winston: New York.

Grunig JE. 2000. Collectivism, collaboration, andsocietal corporatism as core professional valuesin public relations./oMrna/ of Public RelationsResearch 12 : 23 -48 .

Grunig JE. 2001.2-Way sym metrical public relations,past, present & future. InHandbook of PublicRelations, Heath RL (ed.). Sage: London.

Harrison S. 1995. Public Relations An Introduction.Intemational Tho mps on Business Press: London.

Hendrix JA. 1988. Public Relations Cases. IheAmerican University: California.

Hollingsworth M. 1991. MPs for Hire: The SecretWorld of Political Lobbying Bloomsbury:London.

Jaatinen M. 1999. Lobbying Political Issues. AContingency Model of Effective Lobbying Stra-tegies. Inforviestinta Oy: Helsinki,

John S. 2002. The Persuaders: W hen LobbyistsMatter. Palgrave Macmillan: Basingstoke.

Jordan G. 199 1. (ed.). The Commercial Lobbyists:Politics or Proflt in Britain. Aberdeen UniversityPress: Aberdeen.

Kaluski J. 2002 . N-Person stochas tic gam es w ithcoalitions. Cybernetics and Systems Analysis 38 :387-398 .


15/19

98 Freya Aitken-Turff and Nigel JacksonKarlberg M. 1996. Remembering the public inpublic relations research: from theoretical tosymmetry./owmfl/ of Public Relations Research8:263-278.Kearns KD, West WL. 1996. Innovations in publicaffairs programming: collaborative planning andbeyond. In Practical Public Affairs in an Era ofChange. A Comm unications Guide or Business,Govemment and College, Dennis LB (ed.). PRSA:London, New York.Kleindl B. 1999. A game theoretic perspective onmarket-oriented versus innovative strategicchoice. Journal of Strategic Marketing 7: 265-274.Lorrange P, Roos J. 1993. Strategic Alliances,Formations, Implementation and EvolutionBlackwell: Oxford.Lulofs RS, Cahn DD. 2000. Conflict From Theory toAction. (2nd edn). Allyn & Bacon: Needham Heights.MeNair B. 1999. An Introduction to PoliticalCommunication. (2nd edn). Routledge: Londonand New York.Miller C. 2000. Politico's Guide to Political Lobby-ing. Politico's: Oxford, London.Mitehie D. 1998. The Invisible Persuaders. BantamPress: London.Mogel L. 2002. Making it in Public Relations. AnInsider's Guide to C areer Opportunities. (2ndedn). Lawrence Eribaum Associates: London,New Jersey.Moloney K. 1996a. Lobbying a Pluralist Perspective?Or "you said communications; I said politics".Paper to First International Conference onCorporate and Marketing Communications,Keele University, April.Moloney K. 1996b. Lobbyists for Hire. DartmouthPublishing: Aldershot.Moloney K. 1997. Govemment and lobbyingactivity. In Public Relations Principles andPractice, Kitchen P (ed.). Intemational Thomp-son Business Press: London.Moloney K. 2000. Rethinking Public Relations. TheSpin and the Substance. Roudedge: London,New York.Murphy P. 1987. Using games as a model for crisiscommunication. Public Relations Review 13:19-28.Murphy P. 1989. Game theory as a paradigm for the

public relations process. In Public Relations

Theory, Botan CH, Hazleton V Jr (eds). LawrenceEribaum: Hillsdale NJ. Chapter 10.Murphy P, Dee J. 1992. Du Pont and Greenpeace:the dynamics of conflict between corporationsand activist groups. Journal of Public RelationsResearch 4: 3-20.Murray EA, Mahon JF. 1993. Strategic alliances:gateway to the New Europe. Long Range Plan-ning 26: 102-111.Nalebuff BJ, Brandenburger AM. 1996. Co-opeti-tion. Harper Collins Business: London.Olasky MN. 1987. Minimising com petition throughpublic relations. Public Relations Q uarterly 32:9-14.Olsen M. 1965. The Logic of Collective Action:Public Goods and the Theory of Groups. HarvardUniversity Press: Cambridge, Mass.Perloff RM. 1993. The Dynamics of Persuasion.Lawrence Eribaum A ssociates: New Jersey.Plowman KD. 1998. Power in conflict for publicrelations./oMma/ of Public Relations Research10: 237-261.Plowman KD, Briggs WG, Huang Y. 2001. Publicrelations and conflict resolution. InHandbook ofPublic R elations, Heath RL (ed.). Sage: London.

Chapter 23.Rasmusen E. 1993- Lobbying when the deeisionmaker can acquire independent information.Public Choice 77 : 899-913.Rose H. 1991. Case Studies. In Handbook forResearch Students in the Social Sciences, AllanG, Skinner C (eds). Falmer Press: London.Rowell A. 2002. In Battling Big Business. Counter-ing Greenwash & Other Forms of CorporateBullying, Lubbers E (ed.). Greenbooks: Devon.Chapter 3.Sloop R. 1997. Lobbying when the decision-makercan acquire independent information: a com-ment. Public Choice 91: 199-207.Smith MJ. 1993. Pressure, Power and PolicyWheatsheaf: London.Souza C. 1998. So You W ant to be a LobbyistPolitico's: London.Tansey S. 2000. Politics: the Basics Routledge:London.Ury W. 1991. Getting Past No. Business Books Ltd:London.Van Drew C,Van De Vliert E. 1997. Using Conflictin o rganisations. Sage: London.


16/19

A mixed motive approach to lobbying 99Vasquez GM. 1996. Public relations as negotiation: Kong. Internationat fournal of Physical Dis-an issue development perspeetive. fournal of tribution & Logistics Managem ent 29: 7-Public Relations Research 8: 51-11. 21.WhitelyP, Winyard S. 1987. Pmw Mre/or^/be Poor. Yin R. 1989. Case study research: design andRoutledge: London. methods revised. Sage: London.WongA,TjosvoldD, Wong WYL, Liu CK. 1999. Co- Zeigler H, Baer M. 1969. Lobbying: Interactionoperative and competitive conflict for quality and Influence in American State Legislatures.supply partne rships between China and Hong Wadsw orth: Belmont CA.


17/19

10 0 Freya Aitken-Turff a nd Niget JacksonAppendix One mathematicalgame theory explanationZero-sum gamesIn a zero-sum gam e, player's interests are exac topposi tes. The games are based on pureconflicteach player is motivated to harmtheir opponent as everything their opponentloses, the player gains.In the m odel below (Figure Al ) a maximumof ten points are available. Player one hasselected strategies that have given him/her apayoff of seven. This means that player2 can only score a maximum of three out often points .

However, player 2 is unlikely to select astrategy that would allow player 1 to score somany points. The payoff matrix (a frameworkfor analysing what each strategy will costboth players) for this game is shown inFigure A2:The columns of the matr ices show w hat theplayer at the top of the matrix will win (andeverything that a player wins, their o pp on ent

must lose due to the zero-sum nature of thegame). The corresponding strategies alw^aysadd up to ten. If Player 1 selects strategy D an dPlayer 2 selects strategy Q the payoffs will bethree p oints for Player 1 and seven p oints forPlayer 2 (totalling ten points).Strategy D offers the highest payoffs forPlayer 1, however. Player 2 is unlikely to playstrategy P or strategy S as both w ou ld costPlayer 2 too much. Therefore, the best overallstrategy is B because it offers a reasonably high

return w ithou t th e high risks of strategy D. T hehighest payoff strategy for player 2 is R, asPlayer 1 know^s strategy B is the best thatPlayer 1 can achieve w ithou t losing too m anypoints .

I>PLAYER ONEP 10Q 2R 3S 1 2

B5656 4

C6216

D101310Optimal Strategy forPlayer one = B

1 PLAYER TWO PW 1 A 1 1 0^ B 5ac | C | 4>^ 0 l o

Q8489

R7597 4

S84402 Optimal Strategy for- 1 Player two = R

Figure A2. Payoff matrix for zero-sum games.Pure Co-operaiionPlayer OnePlayer TwoPlayer n

1 2 3 4 5 6 7 8

W

9 10

Figure A3. Model of pure co-operation.

Non-zero-sum gamesIn reality, very few games are zero sum innature (Nalebuff and Brandenburger, 1996).They fall into two broad categories: Pure Co-operation Games and Mixed Strategy Games.In a game of pure co-ordination, or co-operation the players receive equal payoffs.The players' interests are so aligned that theycanno t achieve their goals withou t each other .Figure A3 show s a game of pure co-operation,no ma tter how many players join the game theywill always receive the same payoffs:Mixed motive gamesIn this game (mode lled in Figure A4), if playerone passes beyond the win-win zone, theplayer will start to lose payoffs. For example if

ZeroSumPlayerOne FlayerTw o

0

10

1

9

2

8

3

7

4

6

5

5

6

4

7

3

8

2

9

1

Figure Al. Zero-sum model.


18/19

A mixed motive approach to lobbying 10 1

PlayerOnel | 2 3 4 5 6 7i \

v/ln win zonei t > ! 1 0 1 9 1 s 7 6 5 4 3 2 1 Player

Tw oNo deal gone

Figure A4 . Model of mixed strategy games.

players one and two met at a payoff of sixnearest to player 2, player one would losepayoffs as he/she would have conceded toomuch. Likewise if player two progressed on toplayer one's half of the scale, he/she wouldconcede points. The optimal strategy for bo th

players is to work towards the win-winzone. If, when here, the players realizethey cannot achieve their goals simultaneouslythey agree to disagree on a no-deal payoff.This no-deal becomes the players' win-winoutcome.


19/19

Documents

Aiken, Game Theory, 2006