Coupon Advertising Under Imperfect Price Information

Coupon Advertising under ImperfectPrice Information*

JOSE LUIS MORAGA-GONZALEZ´ ´Tinbergen Institute

Erasmus University Rotterdam3062 PA Rotterdam, The Netherlands

[email protected]

EMMANUEL PETRAKIS

University of CreteUniversity Campus at Gallos

Rethymno, Crete, 74100 [email protected]

This paper studies sales promotions through coupons in an oligopoly underimperfect price information. Sellers can distribute either ordinary coupons,

( )or coupon price advertising, or both types of coupons, at distant locationsto attract consumers from their rivals’ markets. A unique symmetric pure-strategy equilibrium exists where rebates and couponing intensity arealways positive. In the ordinary-coupon equilibrium, prices, promotionalefforts, and sellers’ profits are higher than in the coupon-advertising equilib-rium. However, if sellers are allowed to distribute both types of coupons,only coupon advertising is sent out in equilibrium.

1. Introduction

Ž .Coupon advertising or in-ad coupons is being extensively used now-adays by manufacturers and retailers to promote their sales. Anestimated 85% of retailers used in-ad coupons in 1991, according to

* This paper has circulated under the title ‘‘Promoting Sales through Coupons inOligopoly under Imperfect Price Information.’’ We thank very much Helmut Bester,

Ž .Ramon Caminal, Daniel Spulber Editor , and an anonymous referee for many helpful´Ž .comments. Audiences at ASSET 96 Alicante , Jornadas de Economıa Industrial 96´

Ž . Ž .Madrid , and ESEM 97 Toulouse are also gratefully acknowledged for their observa-tions. Any remaining errors are ours.

Q 1999 Massachusetts Institute of Technology.Journal of Economics & Management Strategy, Volume 8, Number 4, Winter 1999, 523]544

Journal of Economics & Management Strategy524

NCH Promotional Services.1 Coupon advertising is a hybrid salespromotion tool with the characteristics of both ordinary coupons andadvertising. In particular, coupon advertising often includes brand

Žinformation product characteristics, location, quality, guarantees,.etc. as well as information about regular prices. At the same time, it

includes a coupon that offers a discount off the regular price. Due tothe twofold feature of in-ad coupons, the effects of coupon advertis-ing on consumers’ behavior, firms’ strategies, and market equilibriacannot be explained by the analysis of ordinary coupons or of adver-tising alone. As the literature has shown, there are various interactiveeffects between the coupon and the print advertisement.2 This litera-ture has restricted attention to the case where coupon advertisingconveys brand information alone. However, casual observation re-veals that coupons often post both the seller’s regular price and itsrebate.3 So far, the literature has paid little attention to couponadvertising that conveys price information.

The purpose of this paper is to analyze sales promotions4 in anoligopolistic market where consumers have imperfect price information.Consumers are uninformed about the price charged at a distant store,and can only learn this price either by venturing, at some cost, to thedistant location, or if they receive price advertisements from thedistant seller. On the other hand, consumers can learn the local priceby visiting the home store at no cost.5 Moreover, consumers areassumed to know the features of all the brands offered in the market.

Ž .1. See Lawrence and Hume 1992 ; they also report that the number of manufactur-Žers’ coupons distributed by supermarkets through their own advertising inserts in-ad

. Ž .coupons increased 700% from 1990 to 1992. Leclerc and Little 1997 report thatapproximately 80% of the over $6.5 billion value of coupons distributed in the United

Ž .States in 1995 were delivered through free-standing inserts FSIs in magazines andnewspapers, and that a coupon in an FSI often appears within an advertisement. Hahn

Ž .et al. 1995 estimated that over 8% of advertisements in major Korean newspapers andmagazines in 1991 were of the sales promotional advertising type.

Ž .2. Leclerc and Little 1997 investigate whether the content of the print advertise-ment influences the effectiveness of the coupon. They found experimental evidencethat the executional cue on the print advertisement can enhance brand attitude, as

Ž . Ž .suggested by Schultz et al. 1993 . Hahn et al. 1995 obtain similar results for theKorean markets.

Ž3. For instance, by visiting Web sites such as www.savecoupons.com or.www.hotcoupons.com , we observe that cybercoupons posting the regular price are

usually offered by pizza stores, car and limousine services, dry-cleaning and laundryservices, etc. Moreover, casual observation reveals that the same type of sellers oftensend, via direct mail, coupon advertising to consumers living in distant neighborhoods.

4. For a detailed description of various methods of sales promotion used by firms,Ž .see, e.g., Kotler 1994 .

5. We thus refer to a locationally segmented market. The same analysis, however,applies to a market that is segmented due to consumers’ brand loyalty. Note that thekey feature in our analysis is the informational segmentation of the market.

Coupon Advertising under Imperfect Price Information 525

Sellers can attract consumers from the rival’s location by sending outcoupons with, or without, advertising their regular price on the

Ž .coupon. That is, sellers can issue two types of coupons: 1 ordinaryŽ .coupons, i.e., coupons simply offering a discount, and 2 coupon

advertising, i.e., coupons including price advertisements. Both typesof coupons serve as a price discrimination device.6 However, couponadvertising also conveys price information, a role of coupons that hasbeen neglected in the literature. Note that, if the costs of issuing andhandling coupons are the same as the costs of advertising, couponadvertising offering a zero rebate is equivalent to price advertising.

Our paper is thus related to two strands of the sales-promotionliterature. The first is the literature on coupons as price discrimina-

Ž .tion devices under perfect price information. Narasimhan 1984 ana-Ž .lyzes the case of a competitive firm, whereas Bester and Petrakis BP

Ž . Ž .1996 and Shaffer and Zhang 1995 consider oligopolistic marketswhere consumers are differentiated with respect to their brand loy-alty or location. The second is the literature on advertising under

Ž .imperfect price information. Stegeman 1991 studies price and prod-uct advertising in a competitive market. In a monopoly model, BesterŽ . Ž .1995 considers price advertising, and Caminal 1996 studies priceadvertising and couponing in the presence of imperfect cost informa-

Ž . Ž .tion. Stahl 1994 and Peters 1984 analyze a homogeneous industryunder imperfect brand and price information, whereas NarashimanŽ . Ž . Ž1988 and BP 1995 analyze price advertising in locationally or due

.to brand loyalty segmented markets. With the exception of CaminalŽ .1996 , the effects of coupons and price advertising have been ana-lyzed in separate streams in the sales-promotion literature.

Our model combines these two strands of literature by inves-tigating firms’ couponing strategies and market equilibria in a lo-

Ž . Ž .cationally as in BP, 1996 and informationally as in BP, 1995segmented market. In addition, our imperfect-price-informationframework allows us to consider price advertising, coupon advertis-ing, and ordinary coupons simultaneously. We show that a symmet-ric pure-strategy equilibrium exists whenever the sellers are allowedto distribute either coupon advertising alone, or ordinary couponsalone, or both types of coupons simultaneously. In equilibrium,sellers always send out coupons to the distant location to attract

Ž . Ž . Ž .6. See, e.g., Narasimhan 1984 , Caminal 1996 , Bester and Petrakis 1996 , andŽ .Shaffer and Zhang 1995 . In this case, coupons foster competition. Coupons may also

Ž .motivate retail participation in price promotions Gerstner and Hess, 1991 , or createŽswitching costs under repeated purchases Banerjee and Summers, 1987; Caminal and

.Matutes, 1990 . Contrary to the first case, competition is now relaxed.


consumers from their rivals’ markets, and thus increase their profitsby price-discriminating between coupon holders and nonholders.

Contrary to the price-advertising literature, where price reduc-tions are temporary,7 sales promotions are permanent when carriedout through coupon advertising or ordinary coupons.8 As all ourequilibria are in pure strategies, sellers always offer price discountsby distributing coupons to the consumers in distant locations. More-over, in the coupon-advertising equilibrium, the sellers’ regular pricesare also permanently advertised. Interestingly, as equilibrium rebatesare positive, sellers will never send out price advertisements if theyare able to promote their sales through coupons. This result holdseven if the costs of issuing and handling coupons are higher than theprice-advertising costs. Therefore, our prediction is that price adver-tising should not be observed in locationally and informationallysegmented markets unless the advertising costs are low enough.

Sellers’ profits are higher in the ordinary coupon equilibriumthan in the coupon-advertising equilibrium, and the latter are higher

Žthan in the equilibrium under perfect price information as in BP,.1996 . As coupon advertising conveys price information, it decreases

informational asymmetries among consumers and thus fosters com-petition. Equilibrium prices, rebates, and couponing intensity arelower when sellers send out coupon advertising rather than ordinarycoupons. Obviously, if consumers are fully informed about all pricesin the market, then equilibrium prices, rebates, and couponing inten-sity are lower than under imperfect price information.

If sellers are allowed to send out both types of coupons, weshow that they promote their sales by distributing only coupon

Ž .advertising in equilibrium. Indeed, Oskin 1993 , in his guidelines forsmart coupon marketing, advises retailers to print the regular priceon the coupon together with the cents-off discount. The sellers wouldprefer to distribute ordinary coupons alone, since in this way theirprofits are higher. However, an individual seller, by advertising his

Ž . Ž . Ž . Ž .7. For example, in Shilony 1977 , Varian 1980 , Narasimhan 1988 , and BP 1995 ,the only symmetric advertising equilibrium is in mixed strategies. The intuition is thatan individual seller can gain by advertising his price only if he offers a lower pricethan his rival’s. Obviously, this cannot be simultaneously fulfilled for all sellers in asymmetric pure-strategy equilibrium. This literature gives a dynamic interpretation to

Žthe mixed-strategy equilibria, arguing that temporal price dispersion occurs as each.store varies its price over time .

Ž .8. According to Kotler 1994 , many products such as soft drinks and cereals areŽ .permanently on sale. Litwak 1996 reports that for some product categories, price

reductions have become the norm and sales at the everyday price the rarity. WorldWide Web coupons are an example of permanent promotions, since consumers can

Ž .print and use them at any moment. Oskin 1993 , who provides guidelines for smartcoupon marketing, suggests that the sellers should send coupons, via direct mail, overand over again so that the new coupon arrives just before the old one expires.


Ž .regular price besides offering a rebate in the distant location, cansteal business from his rival and thus increase his profits. Sellers findthemselves into a prisoner’s-dilemma situation, and hence attainlower profits in equilibrium. Therefore, our analysis predicts thatordinary coupons should not be observed in markets presentinglocational as well as informational segmentation.

The rest of the paper is organized as follows. Section 2 describesthe model. Section 3 and Section 4 characterize the symmetric pure-strategy equilibria when sellers are allowed to send out couponadvertising alone and ordinary coupons alone, respectively. Section 4also compares the above two market equilibria and the equilibriumunder perfect price information. Section 5 extends the model byallowing sellers to issue both types of coupons and shows that, inequilibrium, sellers only send coupon advertising. Section 6 containscomparative-statics and welfare results. Section 7 concludes. All theproofs are relegated to the Appendix.

2. The Model

Ž .As in BP 1996 , we consider a market with two firms, A and B,located in different regions. Firms produce a homogeneous good atzero cost. The neighborhood of each firm is inhabited by a unit massof consumers who have unit demands and a common reservationutility v ) 0. A consumer j can costlessly visit the store at his homelocation, but incurs a transportation cost s G 0 to visit the distantj

w xstore, where s is uniformly distributed on 0, s . To avoid localjmonopolies, assume that v ) s, i.e., transportation costs are not toohigh.

Consumers are aware of the existence, characteristics, and avail-ability of both goods and can learn at no cost the price charged attheir home location. Consumers are uninformed about the pricecharged at the distant location, and can only learn this price either byventuring to the distant store at a certain cost, or if the distant selleradvertises his price. Firms can promote their sales by distributingcoupons in their rivals’ regions. Under our imperfect price informa-

Ž .tion setting, sellers can issue two types of coupons: 1 couponadvertising, i.e., coupons that offer a rebate and, at the same time,

Ž .advertise the regular price, and 2 ordinary coupons, i.e., couponsthat only offer a discount. Both types of coupons serve as a pricediscrimination device,9 as sellers can charge different prices to con-sumers from distinct locations. Coupon advertising also serves as a

Ž . Ž . Ž .9. As in BP 1996 , Caminal 1996 , Narashiman 1984 , and Shaffer and ZhangŽ .1995 .


vehicle to transmit price information as firms inform distant con-sumers about their regular prices. Note that a coupon advertisingoffering a zero rebate is equivalent to pure price advertising.

w xFormally, seller i sends out coupons to a fraction l g 0, 1 ofi

the consumers at location j, offering a rebate r on his regular pricei

p ; 0 F r F p , i s A, B.10 Without loss of generality, let 0 F p F v,i i i i

i s A, B. Since individual transportation costs are unobservable, li

represents the probability that any consumer in region j receives acoupon. Consumers in region j receiving a coupon from firm i canbuy the good at price p y r , while the rest have to pay p . To reach ai i i

Ž .fraction of consumers l, a seller incurs a cost k l . Following theŽliterature see, e.g., Butters, 1977; Grossman and Shapiro, 1984; BP,. Ž .1995, 1996 , we assume that k ? is increasing and convex, and that

Ž . 11k 0 s 0.

3. Coupon-Advertising Equilibrium

In this section we assume that sellers can only send out couponadvertising. Firms compete in the market by simultaneously choosing

Ž .their prices, rebates, and intensities of couponing. Let x s p , r , l ,i i i i

i s A, B, denote seller i’s marketing strategy. Firm i chooses x toi

maximize its profits, taking as given its rival’s strategy.We first determine firm i’s demand and profits. We distinguish

four types of buyers. First, a consumer located at A receiving acoupon advertising from B learns firm B’s regular price and rebate.He then buys at his home store if p F p y r q s and v G p .A B B A

Second, a consumer at A not receiving firm B’s coupon purchases atA whenever p F pe q s and v G p , where pe is the price he expectsA B A B

to be charged at store B. Third, a consumer at B having a couponfrom A learns firm A’s price and rebate. He switches store and buysat A if p y r q s F p and v G p y r q s. Finally, a consumer atA A B A A

B not receiving a coupon from A buys at store A if pe q s F p andA B

v G pe q s, where pe is his expected price at A. Then firm A’sA A

10. It can be checked that in our model sellers cannot increase their profits bydistributing coupons to their home locations.

11. Note that we implicitly assume that printing the price on a coupon has no extracost, i.e., coupon advertising and ordinary coupons are equally costly.


profits are

p y peA BŽ . Ž .P x , x s p 1 y l max 0, min 1 y , 1A A B A B ½ 5½ 5s

Ž .p y p y rA B Bq p l max 0, min 1 y , 1A B ½ 5½ 5s

Ž .p y p y rB A AŽ .q p y r l max 0, min ,A A A ½½ s

Ž .v y p y rA A, 15 5s

p y pe v y peB A AŽ .q p 1 y l max 0, min , , 1A A ½ 5½ 5s s

Ž . Ž .y k l . 1A

By symmetry, firm B’s profits are given by an analogous ex-pression. We shall restrict attention to symmetric Nash equilibriawhere uninformed consumers anticipate correctly the prices chargedby the distant firm.

Ž U U .Definition 1: A pair of marketing strategies x , x is a symmetricA BŽ . Ž U U . Ž U .pure-strategy equilibrium if i P x , x G P x , x for all x /i i j i i j i

U Ž . U U Ž . e Ux , i / j, i, j s A, B, ii x s x , and iii p s p , i s A, B.i A B i i

Ž .Condition i says that each marketing strategy is a best reply toŽ . Ž .the rival’s. Condition ii imposes symmetry. Finally, condition iii

requires consumers’ price expectations to be fulfilled in equilibrium.Ž .Let x s p, r, l denote the symmetric equilibrium market strategy.

The following proposition characterizes the interior equilibrium withcoupon advertising and provides conditions for its existence.

Proposition 1: If sellers promote their sales by sending out couponadvertising, a unique interior symmetric pure-strategy equilibrium12 exists

X X 2Ž . Ž . Ž . Ž .if and only if a k 1 ) sr9 and b k 2 sr3v - v r4 s. This equilib-

12. We are unable to prove, or disprove, the existence of an asymmetric pure-strategy equilibrium in the general case. In a candidate asymmetric equilibrium, ifp - p then it must also hold that l - l ; that is, the seller with the higher priceA B A Bmust distribute more coupon advertising. A number of simulations that we have

Ž . aconducted using the family of couponing costs functions k l s ml , a G 2, indicatethat the above conditions cannot hold simultaneously, and thus an asymmetric equilib-rium fails to exist.


rium is given by the unique solution to the following system of equations:

X2 Ž . Ž .p s 2 sr3l, r s 0.5p , p r4 s s k l . 2a, b, c

w xIn equilibrium, a fraction min 1, 1r3l of consumers redeem their couponsat the distant store, while the rest buy from their home store at the regularprice.

The equilibrium price and coupon-advertising intensity areshown in Figure 1. The downward-sloping curve PP depicts equationŽ . Ž .2a and the upward-sloping curve KK depicts equation 2c . Theintersection of these two curves provides the equilibrium price and

Ž . Ž .coupon-advertising intensity point E . The role that conditions aŽ .and b play in guaranteeing an interior solution can easily be seen in

Figure 1.13

The fact that a pure-strategy equilibrium exists when sellerssend out coupon advertising suggests that sales promotions arepermanent under imperfect price information. This contrasts with theexisting literature, where sales promotions are temporary.14 In this

FIGURE 1.

13. Clearly, if marginal couponing costs are too low, sellers will set lU s 1, while ifthey are too high, sellers will charge p s v to appropriate the entire home consumers’

Ž .surplus with or without sending out coupons to the distant location .Ž . Ž . Ž . Ž .14. See Shilony 1977 , Butters 1977 , Varian 1980 , Narasimhan 1988 , Stahl

Ž . Ž .1994 , and BP 1995 .


literature a pure-strategy equilibrium fails to exist and the equilib-rium in mixed strategies is interpreted as if each store were varyingits price over time. In this sense, sales promotions generate temporalprice dispersion as sellers advertise their prices only with someprobability at each date.

In equilibrium the rebate is strictly positive and, in particular,equals half the regular price.15 As a coupon offering zero rebate isequivalent to pure price advertising in our model, Proposition 1predicts that pure price advertising should not be observed in mar-

Žkets with both informational and locational e.g., due to brand loy-.alty segmentation.

One might argue, however, that handling coupon advertisinggenerates extra costs for the seller, and thus sending out priceadvertisements is significantly cheaper than distributing couponsŽ .see, e.g., Caminal, 1996 . It can be shown that if the price-advertisingcosts are much lower than the coupon-advertising costs, the market-ing strategies of Proposition 1 will no longer constitute an equilib-rium, provided that the costs of couponing are sufficiently convex.Consider an extended model where sellers can send out both pureprice advertising and coupon advertising. Let the advertising costs be

Ž . Ž .k l s d k l , 0 F d - 1. Note first that price advertising and cou-Apons cannot coexist in a symmetric pure-strategy equilibrium. Theintuition is simply that by advertising his price, a seller can attractconsumers from the distant location only if he offers a lower pricethan his rival’s. This however cannot happen simultaneously for all

Ž .the sellers in a symmetric pure-strategy equilibrium see BP, 1995 .Now if d is sufficiently small, an individual seller may find itprofitable to deviate by lowering his price and advertising the lowerprice to all the consumers at the distant location. It can be shown that,if the equilibrium couponing intensity is not too high, such a devia-tion will be profitable for the seller. Then the marketing strategies inProposition 1 cannot be sustained as an equilibrium in the extendedmodel.

4. The Equilibrium with Ordinary Coupons

Assume now that sellers can only promote their sales by sending outordinary coupons. We first determine seller A’s profits. As previ-

15. This is due to our assumption that transportation costs are uniformly dis-tributed. It can be checked that if their distribution is biased towards low-transporta-

Ž .tion-cost consumers e.g., s is distributed exponentially , the equilibrium rebate is lessthan half the regular price.


ously, four different groups of consumers can be distinguished. Aconsumer at A receiving firm B’s coupon learns only the rebateoffered by firm B. He buys at A if p F pe y r q s and v G p . AA B B Aconsumer at A not receiving firm B’s coupon purchases at his homestore whenever p F pe q s and v G p . A consumer at B whoA B Areceives a coupon from A only learns the rebate offered by firm A.He switches store and buys at A if pe y r q s F p and v G pe yA A B Ar q s. Finally, a consumer at B not receiving firm A’s coupon buysAat A if pe q s F p and v G pe q s. Firm A’s profits are thenA B A

p y peA BŽ . Ž .P x , x s p 1 y l max 0, min 1 y , 1A A B A B ½ 5½ 5s

Ž e .p y p y rA B Bq p l max 0, min 1 y , 1A B ½ 5½ 5s

Ž e .p y p y rB A AŽ .q p y r l max 0, min ,A A A ½½ s

Ž e .v y p y rA A, 15 5s

p y pe v y peB A AŽ .q p 1 y l max 0, min , , 1A A ½ 5½ 5s s

Ž . Ž .y k l . 3A

Firm B’s profits are analogous by symmetry. The followingproposition characterizes the equilibrium with ordinary coupons.

Proposition 2: If sellers promote their sales by sending out ordinarycoupons, a unique symmetric interior pure-strategy equilibrium exists if and

X X 2Ž . Ž .only if k 1 ) sr4 and k srv - v r4 s. This equilibrium is given by thesolution to the following system of equations:

X2 Ž . Ž .p s srl, r s 0.5p , p r4 s s k l . 4a, b, c

w xIn equilibrium, a fraction min 1, 1r2l of consumers redeem coupons atthe distant store, while the rest buy from their home store at the regularprice.

In Figure 1, the equilibrium price and couponing intensity areX X Ž X .given by the intersection of curves P P and KK point E . Equation


Ž . X X Ž .4a is depicted by P P , while KK represents equation 4c , which isŽ . X Xthe same as 2c . Note that P P lies entirely above PP.

As in the coupon-advertising equilibrium, sellers always offerpositive rebates that are equal to half the regular price in equilibrium.Moreover, sales promotions are not temporary, since coupons offer-ing rebates occur in a pure-strategy equilibrium.

Ž .It is interesting to compare our results Propositions 1 and 2Ž .with those under perfect price information BP, 1996 . The equilib-

Žrium under full information is characterized by three equations see.their Proposition 1 . Their last two equations coincide with the corre-

sponding equations of both of our equilibria. The only difference liesin the first equation: under full information, the equilibrium price is

Y YŽ .given by p s sr 1 q 0.5l , which is depicted by P P in Figure 1. AsKK is common to all cases, EY in Figure 1 represents the equilibriumprice and advertising intensity under perfect price information. Notefurther that PYPY lies entirely below PP.

Interestingly, the equilibrium rebate equals half the regularŽ .price r s 0.5p under both imperfect and perfect price information.

In all these cases, r is chosen to maximize the seller’s profits obtainedfrom those consumers receiving a coupon. Since coupon advertisingalso conveys price information, this part of the maximization problem

Ž .in Proposition 1 is identical to the corresponding one in BP 1996 . Onthe other hand, a consumer receiving an ordinary coupon does notlearn the regular price of the good. Then the equilibrium discountequals half the expected regular price. However, since consumersanticipate correctly the price charged at the distant location, thediscount equals half the regular price.

Further, we observe from Figure 1 that equilibrium prices andcouponing intensities are higher whenever price information is im-

Ž Y X .perfect E lies to the southwest of both E and E . Obviously,imperfect information generates informational segmentation and thusreduces price competition. Firms can then send out coupons to moreconsumers at the distant store without having to cut their regularprices substantially. Interestingly, the price differential between theordinary coupons and the perfect-price-information equilibrium de-

w XŽ .creases as marginal costs of couponing decrease as k l decreases,xKK shifts to the right . Firms with lower marginal costs can send out

coupons to a bigger fraction of consumers, and thus decrease theinformational segmentation of the market. In fact, if the marginalcosts of couponing are sufficiently low, the coupon-advertising equi-librium converges to that under full information. On the other hand,the ordinary-coupon equilibrium always involves higher prices and


Žadvertising intensities than the coupon-advertising equilibrium EX.lies to the southwest of E . The intuition is that sellers, by using

coupon advertising instead of ordinary coupons, spread price infor-mation, and thus reduce informational segmentation and increasecompetition in the market. Then to avoid a substantial reduction ofhis regular price, a seller optimally reduces his sales-promotionintensity.

Finally, we compare sellers’ profits in the three equilibria. Ourprevious discussion reveals that sales-promotion costs are higher inthe ordinary-coupon equilibrium than in the coupon-advertisingequilibrium, and the latter are higher than those under perfect priceinformation. The same is true for the regular prices and rebates, whilethe opposite holds for the sales-promotion intensities. As a result,

Ž .sellers’ revenues and hence profits are not easily comparable acrossequilibria. The following proposition compares equilibrium profitsfor a family of cost functions that is common in the literature.

Ž . aProposition 3: If k l s ml , a G 3, then equilibrium profits arehigher under ordinary coupons than under coupon advertising, and thelatter are higher than under perfect price information.

The intuition is that as the information available in the marketincreases, sellers face stronger price competition, and thus typicallyobtain lower profits. Note however that, as the market becomes moreinformed, there is also less need for firms to spend on price ads.Finally, equilibrium profits under coupon advertising approach thoseunder perfect information as the marginal cost becomes small, whilethe equilibrium profits under ordinary coupons always remain higher.

5. A Model with Coupon Advertising andOrdinary Coupons

So far we have assumed that sellers can promote their sales bysending out either coupon advertising or ordinary coupons. We haveseen that sellers’ profits are typically higher when they distributeordinary coupons. A natural question then arises: If sellers can use

Ž .both coupon advertising and ordinary coupons, what type s ofcoupons will be distributed in equilibrium? The following proposi-tion answers:

Proposition 4: If sellers can send out both coupon advertising andordinary coupons to promote their sales, then ordinary coupons will never


be distributed in equilibrium. The unique symmetric equilibrium in purestrategies is the coupon-advertising equilibrium described in Proposition 1.16

Our model predicts that ordinary coupons should not be ob-served in markets that are both locationally and informationallysegmented. As we have seen, both sellers would earn higher profits ifthey could agree to send out ordinary coupons alone. However, anindividual seller, by lowering his price and informing consumers atthe rival’s location about this reduction, is able to attract morecustomers and thus increase his profits. Thus, whenever the rivaldistributes ordinary coupons alone, the seller has an incentive to sendout coupon advertising to the distant location. Sellers find themselvesin a prisoner’s dilemma, and thus obtain lower profits in equilibrium.

Interestingly, in the unique symmetric pure-strategy equilib-rium, sellers send out only coupon advertising to the distant location.The intuition is as follows. A deviation from the equilibrium market-

Ž .ing strategy described in 2a, b, c can only be profitable if, e.g., sellerA, who decides to send out ordinary coupons as well, raises his

Ž .regular price. Let p ) p be his regular price, r the rebate offeredA Ain coupon advertising, and rX the rebate of an ordinary coupon. TheAkey to our argument is how consumers who unexpectedly receive an

Ž . eordinary coupon form their out-of-equilibrium expectations p . InAequilibrium, those consumers expect to receive either a coupon withthe price printed on it or nothing. They receive, instead, an ordinarycoupon, which moreover offers a rebate different from the equilib-rium rebate. Rational consumers, however, know that the deviatorsets its rebate in an optimal manner for any regular price chosen.Hence, those consumers receiving an ordinary coupon form rationalout-of-equilibrium beliefs, and can thus infer the regular price fromthe rebate printed on the coupon. In fact, these expectations are theonly ‘‘consistent’’ beliefs based on their information. In particular, aconsumer in region B receiving an ordinary coupon observes rX andAcan infer the equilibrium price p; he also knows that seller A will setoptimally his regular price and rebate, taking as given consumersexpectations pe . That is, the consumer, knowing seller A’s optimalA

X Ž e .rule, r s 0.5 p q p y p , can conduct a simple thought experi-A A Ament and infer the only regular price p that is consistent with hisA

Ž .own beliefs see also footnote 19 . This, in turn, implies that con-sumers receiving ordinary coupons behave in the same way as thosereceiving coupon advertising. Hence, if seller A did not have anincentive to deviate by raising his price in the equilibrium with

16. The proof of Proposition 4 is available from the authors upon request.


coupon advertising, he does not have an incentive to increase hisprice when sending out ordinary coupons either. Therefore, thisdeviation cannot be profitable.17

6. Comparative Statics

Figure 1 allows us to derive comparative-statics results for thecoupon-advertising equilibrium of the extended model. We first study

Žthe effect of the degree of product differentiation measured by the.size of transportations costs, s on the equilibrium outcome. An

increase in s shifts the ‘‘curve PP ’’ to the right and the KK to the left.ŽThen, in line with the literature see, e.g., Perloff and Salop, 1985;

.Shaked and Sutton, 1982 , the equilibrium price increases with thedegree of product differentiations. Moreover, the equilibrium

w Ž .couponing intensity increases with s since from 4 we see thatX Y2 Ž . Ž . xs s 9l k l and k l ) 0 . The equilibrium redemption rate, how-

Ž .ever, weakly decreases with increasing s. Since only the consumerswith transportation costs lower than or equal to the rebate r redeem

w x w xtheir coupons, the redemption rate equals min 1, rrs s min 1, 1r3l .Therefore, although more consumers receive a coupon, a smallerpercentage of them redeem it.

Ž . XŽ .Finally, from 2 we get p s 6lk l , and the equilibrium profitsX2 Ž . Ž . Ž .become P s p y l p r4 s y k l s 5lk l y k l . Thus, sellers’

Xw Ž .profits increase with s since l increases with s and Prl s 4k lYŽ . xq 5lk l ) 0 . The intuition is simple. As s increases, it becomes

more difficult to attract consumers from the distant location. Ascompetition becomes softer, sellers can charge higher prices. On theother hand, sellers increase their couponing effort to motivate moreconsumers to switch stores. Contrary to the first effect, the latterfosters competition. However, the first effect is dominant and thussellers’ profits increase.

We next analyze the effect of marginal couponing costs on theXŽ .equilibrium outcome. As k l increases, the curve KK shifts to the

left, while the curve PP remains unchanged. As a result, the equilib-rium price and rebate rise, while the couponing intensity decreases.In fact, if the marginal cost is prohibitively high, coupons will not beissued, and sellers will extract all the surplus of the local consumers

17. Proposition 4 holds true for other out-of-equilibrium beliefs, too. For instance, itholds if consumers receiving ordinary coupons are ‘‘pessimists,’’ i.e., they believe that

Ž .seller A charges the higher equilibrium price under ordinary coupons. It also holds ifthose consumers are ‘‘optimists,’’ i.e., they believe that seller A did not print the priceon the coupon by mistake, but only if the couponing cost function is sufficientlyconvex.


by charging the monopoly price v. Further, the equilibrium redemp-Ž .tion rate weakly increases with the marginal costs of couponing.

Even though fewer coupons are sent out, a higher fraction is re-deemed because the rebate offered is higher. Finally, to study the

XŽ .effect of an increase in k l on sellers’ profits, we consider the familyŽ . aof costs functions k l s ml , a G 3. Our model confirms the well-

known result in the informative-advertising literature: Sellers’ profitsŽincrease when the marginal costs of couponing rise see, e.g., Gross-

.man and Shapiro, 1984; Peters, 1984; BP, 1995 . While an increase inthe marginal costs, and hence in the total costs of couponing, has anegative direct effect on profits, there is also a positive strategiceffect: Sellers reduce their couponing intensity and thus competitionis relaxed. The strategic effect dominates the direct effect, and thussellers’ profits increase when couponing becomes more expensive.Thus, in line with the literature, sellers would prefer couponing to beillegal in our model too. Summarizing,

Proposition 5:

Ž .a As the degree of product differentiation increases, equilibrium prices,rebates, couponing intensity, and sellers’ profits increase, while equi-librium redemption rates decrease.

Ž .b As the marginal cost of couponing increases, equilibrium prices, re-bates, and redemption rates increase, while equilibrium couponingintensity decreases. Further, equilibrium profits increase with m if the

Ž . acouponing costs are k l s ml , a G 3.

Finally, we turn to the welfare analysis. Since all consumers buyin equilibrium, and production costs are zero, total welfare equals

wgross consumer surplus minus couponing costs, i.e., SW s 2 v yŽ .xk l . Then consumer surplus is obtained by subtracting sellers’ total

XŽ . Ž .profits, 10lk l y 2k l , from total welfare, i.e.,

X Ž . Ž .CS s 2v y 10lk l s 2v y 10 sr9l 5

Xw Ž . Ž . xsince 2a, b, c implies lk l s sr9l . As l increases with s, bothconsumer surplus and welfare decrease with increasing degree ofproduct differentiation. Since sales promotion costs are sociallywasteful in our model, total welfare is higher when sellers spend lesson couponing. Consumer surplus also decreases with increasing s, asa higher degree of product differentiation implies softer competition,and thus higher equilibrium prices. Moreover, as marginal costs ofcouponing increase, consumer surplus decreases. Sellers not onlycharge higher prices, but also send fewer coupons to the distant


location. Finally, to study how an increase in the marginal cost ofcouponing affects total welfare, we consider the family of cost func-

Ž . ations k l s ml , a G 3. As both marginal and total cost of coupon-ing increase, there is a negative direct effect on total welfare, and apositive indirect effect due to less intensive sales promotion. Thedirect effect, however, dominates, and welfare decreases with increas-ing m. Summarizing,

Proposition 6:

Ž .a Consumer surplus and welfare decrease with increasing degree of prod-uct differentiation

Ž .b Consumer surplus decreases as the marginal cost of couponing in-creases. Further, total welfare decreases with increasing m when the

Ž . acouponing costs are k l s ml , a G 3.

7. Conclusions

This paper analyzes the sellers’ sales promotion strategies in marketswhere consumers are uninformed about the prices charged in distantlocations or the prices of other brands. Pizza stores, food delivery,hairdressing, car and limousine services, dry cleaning and laundry,super- and minimarkets, videostores, and electronics are typical ex-

Žamples of markets presenting informational and locational or brand-.loyalty segmentation. Sellers in these markets can attract customers

from distant locations, or from other brands, by targeting coupons tothe customers of their rivals.18 Consumers with low transportationcosts, or low brand loyalty, will switch store only if they receive acoupon and also believe, or know, that the discounted price chargedat the distant store is sufficiently lower than the regular price at the

Žhome location. By printing their regular price on the coupon coupon.advertising , sellers have the option to inform consumers at the

distant location about their undiscounted price at no additional cost.It is shown that sellers’ profits are higher when they distributeordinary coupons instead of coupon advertising. However, an indi-

18. The analysis of the growing panel data on household purchase behavior withthe help of new advanced statistical procedures allows firms to target coupons toselected consumers with considerable accuracy. Catalina Marketing Co. and CiticorpP.O.S. Information Services, as well as some marketing firms and retail chain stores,have created customer databases that are currently used for a more effective targetingof coupons. Moreover, coupons are targeted to selected customers via direct mail. For

Žinstance, Computerized Marketing Technologies, Inc. and Donnelly Marketing Carol. wWright program mail coupons to millions of selected households each year for details

Ž . xsee Shaffer and Zhang 1995 and the references therein .


vidual seller, by lowering his regular price and printing it on thecoupons, can attract more customers from his rival’s location andthus increase his profits. Sellers find themselves in a prisoner’sdilemma. In equilibrium, both sellers promote their sales by sendingout coupon advertising alone, and as a result their profits are lower.

Our model predicts that ordinary coupons should not be ob-served in locationally and informationally segmented markets wherethe coupons are issued by the sellers themselves. Clearly, couponsnot posting the regular price are often distributed in real-worldmarkets. Of course, one reason is that a large number of couponsŽ .about 70%, according to NCH Promotional Services are issued bymanufacturers who sell their goods through distribution channels.For obvious legal reasons, those coupons cannot have the priceprinted on them. Of the remaining 30% of the coupons that are issuedby retailers or manufacturers selling to consumers directly, to the bestof our knowledge, there is no information about the usage rates ofcoupon advertising and ordinary coupons. As most of the reports oncoupon usage are prepared by coupon redemption agents or clearinghouses, retailer-initiated coupon promotions are not included in thosedatabases, because sellers hardly ask for the services of these agents.An empirical test of our findings will be hard to conduct until dataon the usage rates of various types of coupons are available for thosemarkets. Casual observation, however, reveals that both ordinarycoupons and coupon advertising are distributed in those markets.

One possible explanation for the existence of ordinary couponscould be that sellers are colluding in an infinitely repeated marketinteraction. This collusion is, however, partial, since sellers couldfurther increase their profits by not issuing coupons at all, andbehaving as monopolists in their home location. A better explanationmight be that sellers, by printing their regular price on coupons withrelatively large duration, lose their flexibility to modify those prices ifthey face random shocks, such as unexpected demand and costvariations. Sellers then prefer to issue coupons offering discounts aspercentage off the regular price. This subject is open to furtherresearch.

Appendix

Proof of Proposition 1. First, we show that an symmetric interiorŽ .equilibrium satisfies 2a, b, c . Assume, for the moment, that con-

sumers at i not receiving coupons believe that pe G p ; also, thatj ip G p y r , i, j s A, B. We check below that these assumptions arej i i


Žindeed satisfied in equilibrium. Then firm A solves by symmetry,.B’s problem is analogous

Ž .p y p y rA B BŽ .max p 1 y l q p l 1 yA B A B ž /sp , r , lA A A

Ž .p y p y rB A AŽ . Ž . Ž .ql p y r y k l . 6A A A As

Ž .The first order conditions focs are

Ž . Ž .2 p y p y r p y 2 p y rA B B B A A1 y l q l s 0,B As s

Ž .p y 2 p y rB A Ay l s 0,A sŽ .7

Ž .p y p y rB A A XŽ . Ž .p y r y k l s 0.A A As

Ž .Imposing symmetry i.e., x s x s x and using the rational-expec-A BŽ e e . Ž .tations hypothesis i.e., p s p , p s p , we obtain 2a, b, c . NoteA A B B

that all the assumptions made above are satisfied.Ž .We next show that the system 2a, b, c has a unique interior

X X 2Ž . Ž .solution if and only if k 1 ) sr9 and k 2 sr3v - v r4 s. EquationXŽ . Ž . Ž . Ž . Ž .2a defines p l s 2 sr3l with p l - 0, p 0 s `, and p 1 s1 1 1 1

X 0.5Ž . Ž . Ž . w Ž .x2 sr3 curve PP in Figure 1 . Equation 2c defines p l s 4 sk l2X X 0.5Ž . Ž . Ž . w Ž .x Ž .with p l ) 0, p 0 - `, and p 1 s 4 sk 1 curve KK . From2 2 2

Ž . Ž .Figure 1, it can be checked that p l and p l intersect at an1 2interior point such that p F v if and only if the above conditions areverified.

Finally, we check that no firm has an incentive to deviate.Ž .Assume firm B follows the equilibrium strategy p, r, l . If A devi-

ates, consumers at B not receiving a coupon have no reason tochange their expectations, as they remain uninformed of A’s price.Nor do consumers at A have any reason to change their expectationsabout B’s price. We first check A’s incentives to deviate by loweringhis price together with some rebate and couponing intensity. Thereare two cases. First, profits from a deviation such that 0.5p F p F pA


are given by

p y 0.5pAŽ .P s p 1 y l q p l 1 yA A A ž /s

Ž .p y p y rA AŽ . Ž . Ž .q l p y r y k l . 8A A A As

Ž .Since these profits equal those of equation 6 , it is obvious that Acannot gain by adopting such a deviation. Second, if A chargesp - 0.5p, then he obtainsA

Ž .p y p y rA AŽ . Ž . Ž .P s p q l p y r y k l . 9A A A A A As

Firm A would optimally set p y r s 0.5p. Then P rl s 0A A A AX2 Ž .reduces to p r4 s s k l . Thus, A would optimally choose l s l.A A

To complete the argument, note that P r p s 1 ) 0, i.e., profitsA Adecrease as the price falls. Consequently, A would optimally set

Ž .p s 0.5p, which is not a profitable deviation see above . Therefore,AA cannot gain by lowering his price.

We next check A’s incentives to raise its price. Then A’sdeviation profits are

p y p p y 0.5pA AŽ .P s p 1 y l 1 y q p l 1 yA A Až / ž /s s

Ž .p y p y rA AŽ . Ž . Ž .q l p y r y k l . 10A A A As

Seller A would optimally set p y r s 0.5p. Then P rl s 0A A A AX2 Ž .reduces to p r4 s s k l . Again, A would optimally choose l s l.A A

w Ž . xFinally, it can be checked that P r p s p 1 q l y 2 p rs - 0,A A Ai.e., profits decrease as the price increases. As a result, A cannot gainby raising its price. The proof is now complete. IProof of Proposition 2. The first two steps are similar to those in the

wproof of Proposition 1, and we will not repeat them here for detailsŽ .xsee Moraga and Petrakis 1997 . It remains to show that no seller has

incentive to deviate. Assume that B follows the equilibrium strategyŽ . Ž .p, r, l in 4a, b, c , while seller A deviates by choosing p / p. AtAthis point, it is crucial to carefully specify the expectations of con-sumers at B after seller A’s deviation. Consumers at B not receiving


a coupon do not observe anything new; thus, their expectationsremain unchanged. However, those consumers at B getting a couponfrom A should change their expectations whenever they observe arebate different from the equilibrium one, i.e., r / 0.5p. In fact, theyAknow that seller A will set his rebate in an optimal manner, which

Ž e .from the seller foc is r s 0.5 p q p y p . By conducting a simpleA A Athought experiment, they can infer A’s regular price.19 This demon-strates that the out-of-equilibrium expectations of those consumersreceiving a coupon must be rational, i.e., pe s p .A A

First, A deviates by lowering his price such that 0.5p F p - p.AThen his profits are,

p y 0.5pAŽ .P s p 1 y l q p l 1 yA A A ž /s

Ž e .p y p y rA AŽ . Ž . Ž .q l p y r y k l . 11A A A As

From our previous argument, pe s p . Hence, the optimal rebateA Amust satisfy 0.5p s p y r . Further, the couponing intensity has toA A

X2 Ž .satisfy P rl s p r4 s y k l s 0, which implies l s l. As aA A A AŽ .result, P r p s 2l p y p rs ) 0, i.e., profits decrease as pA A A A

decreases; thus seller A cannot gain by setting 0.5p F p - p. Sup-Apose next that A chooses a price such that p - 0.5p. Profits are thenA

Ž e .p y p y rB A AŽ . Ž . Ž .P s p q p y r l y k l . 12A A A A A Ase Ž .As above, p must equal p , and thus r satisfies 0.5p s p y r .A A A A A

Also, P rl s 0 implies that l s l. As a result, P r p s 1.5A A A A A) 0. Thus, A would choose p s 0.5p, which cannot be a profitableA

Ž .deviation see above .Finally, consider that A raises its price, p ) p. Profits are thenA

Ž e .p y p y rA B BŽ .P s p 1 y l q p l 1 yA A B A B ž /s

Ž e .p y p y rB A AŽ . Ž . Ž .q p y r l y k l . 13A A A As

19. Assume that p s 10 and r s 5 in the equilibrium with ordinary coupons.Assume, further, that consumers at B receive a coupon from A offering r s 6. If, forAinstance, they form expectations pe s 12, then those consumers, using the sellers’A

Ž e .optimal rebate rule r s 0.5 p q p y p , infer that p must equal 10. Thus, theirA A A Aexpectations are not correct. The only beliefs consistent with their information are thenpe s 11. In fact, the optimal rebate rule implies that p s 11, thus satisfying pe s p .A A A A


As before, pe s p . Note that these profits equal those where AA A

deviates by choosing 0.5p F p - p. Thus, the optimal rebate andA

couponing intensity satisfy 0.5p s p y r and l s l. Then,A A AŽ . P r p s 2l p y p rs - 0. This proves that A will not raise hisA A A

price. The proof is now complete. I

Proof of Proposition 3. Denote the optimal couponing intensity withcoupon advertising as l, with ordinary coupons as lX, and underperfect information as lY. The firms’ profits are P, P

X, and PY,

X Ž . XŽ .respectively. First, we compare P and P . From 2a, b, c , P s 5lk lŽ . Ž . X X XŽ X. Ž X. Ž . ay k l , and from 4a, b, c , P s 3l k l y k l . For k l s ml ,

X X aŽ . aŽ .a G 3, we have P ) P if and only if l 3a y 1 ) l 5a y 1 , orX wŽ . Ž .x1r a Ž . Ž .l rl ) 5a y 1 r 3a y 1 . Further, from 2a, b, c and 4a, b, c ,

X X 2 X X X2 aŽ . Ž . Ž .s s 9l k l s 4l k l . Then for k l s ml , we have l rl s9 Xa rŽ1qa.Ž . wŽ . Ž. Therefore, P ) P if and only if 2.25 ) 5a y 1 r 3a y4.xŽ1qa.r a1 . This inequality is clearly satisfied for the case a s 3.

Further, since its right-hand side is decreasing in a, it can be checkedthat P

X ) P for all a G 3.Y Y ŽSecond, we compare P and P . The latter are P s 4 q

Y . XŽ Y . Ž Y . Ž .l k l y k l see BP, 1996 . Proceeding as before, and given thatY Y X Y Y2Ž . Ž .l satisfies s s 4 1 q 0.5l k l one obtains that P G P if and

only if

Ž .2 ar aq1 aŽay1.rŽaq1.Ž . Ž .5a y 1 2 q l l

2 a rŽaq1.w Ž . ay1 a x Ž .y 3 a 4 q l l y l G 0 14

for all a G 3 and 0 - l - 1. It is clear that in the extreme case l s 1,Y Ž .P s P . By plotting the left-hand side of inequality 14 , it is easily

seen that it is always positive. I

Proof of Proposition 5. It only remains to show that profits area 1rŽ1qa.Ž . Ž .decreasing in m. For k l s ml , a G 3, we have l s sr9am .

1rŽaq1. a rŽaq1.Ž .Ž .Profits are then P s m 5a y 1 sr9a , which increaseswith m. I

Proof of Proposition 6. It only remains to show that welfare is de-Ž . acreasing in m. For k l s ml , a G 3, we have SW s 2v y

a rŽ1qa.Ž . Ž .2m sr9am using the optimal l , which decreases with in-creasing m. I


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Coupon Advertising Under Imperfect Price Information