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1 Les Cahers du GERAD ISSN: Coop Advertsng Programs under Compettve Market Structures Salma Karray Georges Zaccour G Aprl 2003 Les textes publés dans la sére des rapports de recherche HEC n engagent que la responsablté de leurs auteurs. La publcaton de ces rapports de recherche bénéfce d une subventon du Fonds F.C.A.R.

2 Coop Advertsng Programs under Compettve Market Structures Salma Karray Marketng Department HEC Montréal, Canada Georges Zaccour GERAD & Marketng Department HEC Montréal, Canada Aprl, 2003 Les Cahers du GERAD G Copyrght c 2003 GERAD

3 Abstract We examne whether cooperatve advertsng programs could consttute an effectve tool to coordnate compettve marketng channels. Whle prevous studes showed that such programs ncrease total channel profts n blateral monopoles, no evdence of such a result has been provded for channels where competton s present at manufacturng and/or retalng levels. In ths paper, we consder a dstrbuton channel formed of two manufacturers and two retalers and propose a model that accounts for brand and store compettve nteractons. The effcency of the coop plan s nvestgated by comparng Nash equlbra of two non-cooperatve games; one where manufacturers do not offer any promotonal support to the retalers, and one where manufacturers do offer such a support. We show that when competton s ntroduced at a channel level, the effcency of the coop program s no more guaranteed for members who operate at that level. Further, for symmetrc channel members, we fnd that cooperatve advertsng programs are ndeed mplemented only under some condtons on brand and store substtuton rates. Fnally, for all compettve scenaros, we show that cooperatve programs are optmal for consumers. Résumé Cet artcle analyse l effcacté des programmes de publcté coopératve pour coordonner des canaux de dstrbuton où deux marques natonales concurrentes sont dstrbuées dans deux magasns concurrents. Dans la lttérature, ces programmes sont effcents dans des canaux consttués seulement de deux membres. L obectf de cet artcle est d étendre ces résultats au cas de canaux avec compétton. On consdère que chaque détallant engage des dépenses pour la promoton locale des deux produts publcté sur le leu de vente, crculares, etc.) et chaque manufacturer envsage de s engager dans un programme coopératf aux termes duquel l rembourserat aux détallants une part de leurs dépenses promotonnelles. L effcacté du programme promotonnel est étudée en comparant les résultats de deux eux non-coopératfs : 1) les manufacturers n accordent aucune ade fnancère aux détallants et 2) les détallants reçovent une partcpaton des manufacturers dans leurs dépenses promotonnelles. Dans le cas symétrque, les résultats montrent que le programme de publcté coopératve devrat être adopté s les taux de substtuton entre magasns et entre marques sont peu élevés. Dans le cas asymétrque, les résultats montrent que l entrée d un concurrent dans un marché où le manufacturer le détallant) est en stuaton de monopole pourrat menacer l effcacté du programme de coopératon promotonnelle pour ce manufacturer détallant). Mots clés : théore des eux, crcut de dstrbuton, compétton, programme de coopératon promotonnelle. Acknowledgments: Research supported by NSERC-Canada and Drecton de la Recherche HEC Montréal.

4 Les Cahers du GERAD G Introducton A cooperatve advertsng program s a fnancal arrangement n whch a manufacturer pays part of the cost of local advertsng and promoton undertaken by a retaler for hs products Bergen and John 1997). These coop programs are by no mean a margnal phenomenon n dstrbuton channels. Sen 1992) estmated that 25-40% of local advertsements and promotons are funded on a cooperatve bass. Roslow and al. 1993) and Somers and al. 1990) estmate the yearly amount spent on cooperatve advertsng programs by Amercan manufacturers to more than $10 bllon. In 2002, approxmately $60 to $65 bllon are gven by manufacturers to retalers to promote ther products Arnold, 2003). The percentage of the coop cost pad for by the manufacturer seems to vary wth the ndustry, the frms nvolved, etc. Bergen and John 1997) report that applance retalers would get back more than 75% of ther total advertsng dollars from manufacturers, whereas, accordng to Brennan 1988), IBM offers a splt of advertsng costs wth retalers. In the automoble ndustry, GM offers a 25% coop-rate to ts dealers Green 2000) and provded huge amounts to car rental agences : $7-$8 mllon a year to Avs, $2 mllon to Natonal, and $5 mllon to Alamo Rent-A-Car Tenowtz 1992) whle Ford spent $20 mllon on coop funds n 1990 Serafn 1990). In the computer ndustry, Intel has mplemented snce 1991 the world s bggest coop advertsng program Intel Insde wth the collaboraton of computer marketers. The cooperatve funds, earmarked for the promoton of Intel s mcroprocessors, were gven at a bass of 60% partcpaton rate, reached approxmately $800 mllon n 1999 and grew up to $1.5 bllon n 2001 Elkn 2001 and 1999). Another example s that of Mcrosoft who assgned $200 mllon to promote WndowsXP n 2001 and receved much more funds from coop programs ntated by Intel, Compaq, Dell and others Elkn 2001). The relatonshp between a manufacturer and a retaler falls n the classcal blateral monopoly paradgm where barganng models and noncooperatve games have now an establshed tradton. In ths framework, number of contrbutons attempted to assess the mpact of coop programs on such marketng channels. Berger 1972), Dant and Berger 1996) and L and Huang 2001) showed that cooperatve advertsng ncreases total channel profts and retaler s level of local advertsng n a one retaler one manufacturer channel. Ths stpulates that a coop advertsng program can be seen as an ncentve scheme desgned by the manufacturer to mprove channel s effcency as measured by total proft). Recently, some studes consdered the ssue of assessng coop programs and determnng equlbrum partcpaton rule n a dynamc settng where advertsng has some carry over effects. Cooperatve advertsng programs are agan shown to mprove total channel profts for a varety of demand functons and goodwll accumulaton processes Chntagunta and Jan 1992 and Jørgensen and al. 2000). Jørgensen and Zaccour 2002) and Jørgensen and al. 2003) studed, under dfferent assumptons and model formulatons, the relevance of coop programs when retaler s promotons harm the brand goodwll. They showed that the manufacturer may stll fnd t optmal to support retaler s promoton. It has also been shown that one can devse a sde-payment mechansm to ensure that each channel s member s better-off wth the coop program Jørgensen and al. 2001).

5 Les Cahers du GERAD G In the above mentoned papers, the focus s on vertcal coordnaton n channels wthout any horzontal competton. The obectve of ths paper s to explore the relevance of coop advertsng programs n conventonal channels.e. when competton s present, at manufacturng and/or retalng levels. The lterature whch dealt wth the coordnaton problem under such channel s structures were manly concerned wth prcng ssues. The case of a manufacturer dealng wth competng retalers has been studed by, e.g. Jeuland and Shugan 1983), McGure and Staeln 1983), Coughlan 1985), Moorthy 1988) and Ingene and Parry 1995) and Cho 1991) studed a channel wth two manufacturers and one retaler. Recently, some papers explored prcng decsons n conventonal channels wth two manufacturers and two retalers see, e.g. Lee and Staeln 1997, Lal and Vllas-Boas 1998 and Trved 1998). Lookng now at other mechansms than prcng, t s strkng to see how the lterature s sparse although the message from the contrbutons wth a dyad structure was clear that marketng effort could also be a good canddate for coordnatng the channel. Iyer 1998) proposed a spatal model of demand to account for servce and prce decsons of retalers when one manufacturer s leadng the channel. The basc model was then extended to nclude upstream competton between two manufacturers wth the result that coordnaton s not always desrable for channel members. Bergen and John 1997) studed the so-called open-ended coop programs, that s when manufacturers propose a partcpaton rate nto retalers marketng efforts, to study compettve dstrbuton channels. They proposed a model that accounts for competton n retalng wth the am of nvestgatng ts effect on manufacturers coop partcpaton rates. The authors show that the coop advertsng program, along wth a two-part tarff prcng scheme, s an effcent coordnatng mechansm.e. permts to reach the cooperatve soluton). However, they dd not deal wth effcency ssue when upstream competton between manufacturers s ncluded n the model. Km and Staeln 1999) have also studed a conventonal channel but to assess advertsng allowance program that ams to determne a lump sum or sde-payment transfers from the manufacturer to the retaler and the latter pass-through rates. We focus on non-prce competton and assume that retalers choose the level of marketng effort e.g., local advertsng, dsplays, etc.) and manufacturers control ther partcpaton rate nto the retalers marketng efforts f a coop program s an opton. To assess the mpact of the cooperatve advertsng program on the conventonal channel, we shall consder the followng two scenaros: A non-cooperatve smultaneous game where manufacturers do not support the retalers. In ths case, the manufacturers are not actually optmzers and a Nash equlbrum n marketng effort strateges s computed wth two competng retalers as players. Manufacturers outcomes result smply from sellng the equlbrum quanttes to retalers. The result of ths case wll serve as a benchmark. A sequental non-cooperatve game where the manufacturers partcpate n the retalers marketng efforts. In the frst stage, manufacturers play a Nash game and set

6 Les Cahers du GERAD G ther equlbrum coop partcpaton rates. In the second stage, retalers play Nash and determne ther marketng efforts as functons of manufacturers partcpaton rates and equlbrum outcomes result. Ths paper attempts to assess the mpacts of mplementng a cooperatve advertsng program n a conventonal channel for consumers and channel members n terms of marketng efforts, sales and profts. The man results are the followng: Coop advertsng program ncreases retalers marketng efforts. Ths result extends to a compettve settng the one obtaned prevously n a dyad channel. The cooperatve support rates offered by manufacturers to retalers ncrease as brand competton ntensfes and spatal competton decreases. Consumers are always better off when a coop advertsng program s mplemented. Coop advertsng programs do not always mprove channel members profts n a compettve settng. Our fndngs show that a cooperatve plan wll be ndeed mplemented,.e. offered by manufacturers and accepted by retalers, only f the store and brand competton rates are not too hgh. The rest of the paper s organzed as follows. Secton 2 ntroduces the model and Secton 3 derves Nash equlbra for the conventonal channel wth and wthout a coop plan. Secton 4 nvestgates the cooperatve program effcency for some specal stuatons and Secton 5 concludes. 2 Coop Advertsng n a Conventonal Channel Let the conventonal channel be formed of two manufacturers ndexed by = 1, 2) and two retalers ndexed by = 1, 2). In the sequel, we shall use synonymously manufacturer, brand and product as well as retaler, store and outlet. Denote by E retaler s marketng effort e.g., non-prce promotons, local advertsng, n-store dsplay) for brand. Let demand rate Q for brand n store be gven by Q = 1 + E γ 1 θ) E 3 θ 1 γ) E3 θγe3 3,, = 1, 2. 1) where θ, γ [0, 1). The lnear form of our demand functon follows a long tradton of research n modelng channel s strategc prcng decsons n compettve marketng channels McGure and Staeln 1983, Jeuland and Shugan 1988, Cho 1991, Lee and Staeln 1997 and Trved 1998). We adopt a smlar specfcaton to study compettve effects of marketng efforts. The assumpton of the above specfcaton, adapted from Trved 1998), s that the demand for any brand at any outlet depends on marketng efforts for both brands n both outlets. Note that the baselne sales,.e. sales that would occur f none of the brands n none of the stores were advertsed, and the drect margnal effect or effcency) of marketng effort on sales are normalzed to one. The parameter θ captures the degree

7 Les Cahers du GERAD G of product substtutablty and γ the degree of store substtutablty. We assume that the drect margnal effect of marketng effort s hgher than the margnal brand or store substtuton effects, 1 that s 1 γ θ + θγ 0. 2) Note that a suffcent condton for satsfyng the above nequalty s to have θ 1/2 and γ 1/2 whch s obtaned by consderng that effects of marketng efforts for competng product n competng store are lower than the other compettve actons 2 Trved 1998). For the sake of clarty and tractablty and wthout loss of generalty we shall assume n the sequel that ths condton s satsfed. A further nterpretaton of the demand specfcaton could be obtaned from the decomposton of compettve effects. Indeed, expand 1) to get Q = 1 + E γe 3 + θγe 3 θe3 + θγe3 θγe3 3,, = 1, 2. We ) see that an ncremental ncrease n efforts for the competng product n ths store E 3 generates two opposte effects on ts demand rate. On one sde, t decreases demand through a pure product substtuton effect θe3 ), but on the other sde t benefts the demand rate through a cross product-store substtuton effect + θγe3 ). Smlarly, marketng efforts for the same brand n the competng outlet E 3 ) harms demand through a pure store substtuton effect γe 3 ) and ncreases t by a cross-competton mechansm +θγe 3 ). Therefore, an underlyng assumpton of ths demand formulaton s that marketng efforts undertaken by a retaler generate smultaneously postve and negatve effects on the demand rate. Note that ths formulaton extends the one n Bergen and John 1997) and allows for a wder range of postve cross-compettve effects. It consders 1 A smlar assumpton s made n olgopoly theory. Indeed, n prcng models where demand for a frm s gven as a functon of all prces,.e. t s assumed that q = f p 1,..., p n ), f p 1,..., p n) p < 0. meanng that f all frms ncrease ther prce, each one of them wll see ts demand decreasng. Here however, the effect would be postve snce we are dealng wth marketng efforts. 2 Another ratonalzaton for the specfed ranges for γ and θ can be obtaned from an assumpton on margnal rates of substtuton. Indeed, f we assume that Q / E 3 Q / E3 3 Q / E 3 Q / E3 3 then necessarly θ and γ must be less than one half. 1 1 γ γ 1 1 θ θ 1, 1,

8 Les Cahers du GERAD G ndeed postve mpact on demand rate generated by the retaler s efforts for the competng brand n her own outlet. To get yet more nsght nto the functonal form of 1), we dscuss the followng three specal reduced demand models obtaned by settng the product and/or store substtuton parameters at some extreme values: Reduced Model Demand Q Values of θ and γ E θ = γ = E θe 3 θ [0, 1/2], γ = E γe3 θ = 0, γ [0, 1/2] Reduced model 1 corresponds to what has been extensvely studed n the lterature,.e. a dyad marketng channel. In ths context, although the retaler under scrutny may be carryng other products than the brand of the manufacturer and the latter sellng to other retalers, the assumpton s that ths s not relevant to the analyss of the relatonshp between the two protagonsts. The second model stpulates that demand for a brand s a decreasng functon n marketng effort for the competng brand. Ths model better fts the case where the products consdered compete wthn a store and where competton between outlets s rrelevant e.g., the stores operate n non-overlappng terrtores). The last reduced model represents a stuaton where the competton s between stores sellng the same product. Ths model fts probably the case where consumers are already commtted to a brand and the only left decson s where to buy t. For ths segment, t does not really matter f a store s carryng or not an alternatve brand. 3 The full demand model 1) accounts for both substtuton effects and s of nterest to mass dstrbuton ndustres where substtutable brands are sold n competng stores. Admttedly however, ths s not the most general model n the sense that a symmetry assumpton has been made regardng substtuton effects. Indeed, t s readly seen that Q E 3 Q E 3 Q E3 3 = θ 1 γ), = 1, 2. = γ 1 θ), = 1, 2. = θγ,, = 1, 2. We beleve that ths assumpton s acceptable n the context of consumer products belongng to the same category and where the stores carryng them are of the same type. Moreover, symmetrc substtutablty effects are consdered n prevous lterature dealng 3 An llustratve example would be teenagers vstng dfferent stores lookng for a par of sport shoes of ther favorte brand.

9 Les Cahers du GERAD G wth compettve marketng channels Bergen and John 1997 and Trved 1998). However, note that the above assumpton does not mply symmetrc elastctes. Let retaler s marketng efforts cost be gven by the followng convex functon C E, E 3 ) = 1/2w [ E ) 2 + E 3 ) 2], = 1, 2. where w s a postve constant parameter 4. Ths specfcaton has been used n recent lterature dealng wth advertsng decsons 5 Chntagunta and Jan 1992, Chu and Desa 1995, Bergen and John 1997 and Jørgensen and al. 2001). Denote by D the partcpaton rate of manufacturer n the marketng effort cost of retaler. We assume that 0 D 1. To avod prce dscrmnaton, some countres prohbt manufacturers of offerng dfferent partcpaton rates to ther dealers e.g., the Robnson-Patman Act, Secton 3, Act 15, n U.S.A). If ths was to be true, one would then reformulate the model mposng D = D3. Let π be manufacturer s transfer prce, smlar to both retalers, and denote by π the retal prce of brand n store. Snce the model s statc and agan to keep the focus on coop advertsng programs, we assume that these prces are gven constant. Denote by c the unt producton cost of manufacturer. Let m = π c be the margn of manufacturer and M = π π be the margn of retaler on product. In the presence of a coop advertsng program, retaler s proft functon s the dfference between her revenues and her share n the marketng effort costs, that s P = [ M Q 1/2w 1 D ) E ) 2], = 1, 2. 3) where demand rates Q are gven by 1). Smlarly, manufacturer s proft functon s gven by P = [ m Q 1/2wDE ) 2], = 1, 2. 4) 3 Equlbrum Marketng Strateges We now characterze n turn Nash equlbra wthout benchmark scenaro) and wth coop programs and compare them. We shall superscrpt marketng effort equlbrum values and sales n the presence of a coop program by C. Note that n the absence of such program, the manufacturers become passve players and the retalers play a one-stage noncooperatve game. Retaler s optmzaton problem s then gven by max P = MQ E + M3 Q [ 3 ) 1/2w E ) 2 + E3 ) 2], = 1, 2.,E 3 4 Results do not change qualtatvely f we assume brand and store specfc cost parameters. 5 Solutons to a problem wth lnear demand and quadratc advertsng costs s equvalent to those obtaned for a lnear cost problem wth quadratc demand. Hence, even f our demand functon does not account for decreasng margnal effects of marketng efforts, solutons do not change qualtatvely.

10 Les Cahers du GERAD G Proposton 1 In the absence of a coop advertsng program and assumng an nteror soluton, Nash equlbrum marketng effort strateges are gven by E = M M 3 θ 1 γ),, = 1, 2. 5) w Proof. Straghtforward from frst-order condtons. The above result shows that retaler s marketng effort for brand depends on ts margn and compettve brand margn as well as on product and store substtuton parameters. The equlbrum level s determned by the famlar condton statng that margnal cost we ) must be equal to margnal revenue. The latter corresponds to the dfference between the margnal revenue from ths brand M ) and the net margnal revenue or net margnal loss) from the competng brand M3 θ 1 γ)). If ths dfference s negatve, then ths brand wll not be advertsed. Gven the equlbrum levels n 5), one can easly compute manufacturers and retalers profts and also demand rates under ths scenaro. The next proposton summarzes results for the case where manufacturers are actve players and offer coop advertsng programs. In such a scenaro, the game s a two-stage sequental one. Nash equlbrum s determned recursvely by frst obtanng retalers marketng efforts as response functons of manufacturers partcpaton rates and then determnng manufacturers optmal partcpaton rates. Proposton 2 Assumng that the manufacturers offer coop advertsng programs and an nteror soluton, manufacturers and retalers Nash equlbrum strateges are gven by ] ) E C 2m [1 γ 1 θ)] + [M M 3 θ 1 γ) =,, = 1, 2. 6) 2w D = ] 2m [1 γ 1 θ)] [M M 3 θ 1 γ) ],, = 1, 2. 7) 2m [1 γ 1 θ)] + [M M 3 θ 1 γ) Proof. See Appendx. To nterpret the result, we wrte down retaler s response functon ) E C M M 3 θ 1 γ) = ),, = 1, 2. 8) w 1 D

11 Les Cahers du GERAD G and note that the same nterpretaton as for E ) stll holds wth the modfcaton that the margnal cost for the retaler s now w 1 D ) E ) C. It s readly seen from the results of Propostons 1 and 2 that E) C > E and hence coop advertsng programs do ndeed provde an ncentve to retalers to do more marketng effort. The result n 7) shows that the support provded by a manufacturer to a retaler depends on substtuton parameters hence compettve effects are captured) and on hs margn m ) as well as on that retaler s margns on the two products. Note that ths partcpaton rate formula does not nclude the margns of the other manufacturer nether the margns of the other retaler. The partcpaton rate obtaned here generalzes to a compettve settng the ones suggested n a one-manufacturer one-retaler context n Jørgensen and al. 2000, 2001). In these references, the manufacturer also supports hs exclusve retaler f hs margnal revenue s hgher than half of retaler s margnal one. We have here a smlar result wth the dfference that margnal revenues nvolve the substtutablty parameters to account for the compettve channel s structure. From 5) and 8), we get the followng smple relatonshp between the marketng efforts wth and wthout cooperatve support C E) E ) C = D,, = 1, 2. E showng that retaler ncreases the marketng effort for brand at the same rate as the support provded by the manufacturer of that brand. Further, f E ) C > 0, then the denomnator of D s strctly postve. Hence, to have a postve partcpaton rate, we need the followng to hold true m [1 γ 1 θ)] > 1 2 [ M M 3 θ 1 γ) ],, = 1, 2. The rght-hand-sde of the above nequalty s half the margnal revenue of retaler, and the left-hand-sde s manufacturer s margnal revenue. Note also that D < 1 s then automatcally satsfed. The formula provdng the support rates nvolve margns and compettve parameters. The followng two propostons provde the mpact of varyng these parameters on the support rates. Proposton 3 The support rate D,, = 1, 2, s ncreasng n manufacturer s margn; decreasng n retaler s margn on the same brand and ncreasng n that retaler s margn on competng brand; nsenstve to competng manufacturer s and store s margns on both brands.

12 Les Cahers du GERAD G Proof. It suffces to compute the followng dervatves of 7) to get the results: D M D 4 1 γ 1 θ)) X = m X + Y ) 2 > 0, = 2X X + Y ) 2 < 0, D M 3 = 2θ1 γ)x X + Y ) 2 > 0, D M 3 = D M 3 3 = D m 3 = 0. where X = 2m [1 γ 1 θ)], Y = [ M M 3 θ 1 γ) ]. Gven the absence of prce competton and the partcpaton rate formula, the above results are farly ntutve. Each manufacturer s partcpaton rate s ncreasng n hs own margn meanng that as he gans more funds, he has a greater possblty to boost retalers marketng efforts. Further, as a retaler gans hgher margn on a manufacturer s product, she has more avalable funds and could mprove her marketng efforts wth less coop support from that manufacturer. However, a hgher coop partcpaton rate should be offered as the retaler s margn on the competng brand ncreases n order to boost the outlet s revenue through a hgher sales volume. Proposton 4 The support rate D,, = 1, 2, s ncreasng n brand substtutablty parameter; decreasng n store substtutablty parameter. Proof. It suffces to compute the followng dervatves of 7) to get the results: D θ D γ = 4m [ X + Y ) 2 Mγ + M3 1 γ) 2] > 0, 2 [ = m X + Y ) 2 1 θ)y + M3 θx ] < 0. The above results show that the manufacturer s partcpaton rate s ncreasng n product substtutablty and decreasng n store substtutablty. Hence, when competton between brands s tense, manufacturers should adopt an aggressve advertsng behavor and ncrease ther contrbuton to the dealers marketng costs. Further, the more substtutable

13 Les Cahers du GERAD G are the retal stores, the lower should be the support rate, meanng that manufacturers should not encourage store competton by gvng more coop funds to both outlets. It s nterestng to note that Bergen and John 1997) have found the opposte results, albet wthout accountng for postve cross-competton effects of store and brand substtutablty on demand rates. They obtaned ndeed that lower brand substtutablty results n hgher manufacturers margns and therefore nduce the latter to ncrease ther coop partcpaton rates. They also showed that when store substtutablty s tense, there s more need to subsdze local advertsng and hgher coop rates should be provded. 4 Effcency of Coop Advertsng Programs The prevous secton showed that cooperatve advertsng programs ncrease marketng effort of retalers. Although ths may be seen as a postve effect, the central ssue remans however whether or not such programs are effcent. Effcency can be assessed from the pont of vew of consumers and the players nvolved n the channel. Gven that we have assumed constant transfer and retal prces, consumers nterest n such a program could be easly represented by ts mpact on total demand. Players nterest wll be assessed n terms of profts. The followng proposton shows that f consumers have a say n the management of the channel, they wll vote n favor of the establshment of cooperatve advertsng programs. Indeed, t turned out that such programs ncrease total demand rrespectve of the ntensty of substtuton between products and stores. The ratonale s that marketng efforts provde more and better nformaton to consumers and then ncreasng these efforts, thanks to coop programs, boosts demand. Proposton 5 Assumng E ) C > 0,, = 1, 2, coop advertsng programs ncrease total demand. Proof. Usng 5), 6), 1) and computng the dfference n total demand wth and wthout coop advertsng program gves [ Q ) ] C Q = [ E ) ] C [1 γ θ + θγ] E We have establshed that f D 0, then E ) C E 0. It suffces to nvoke assumpton 2) to get the result. An mplementable advertsng program s one whch leads to hgher profts for the partes nvolved. In the realm of one manufacturer one retaler channels, the lterature showed that a coop advertsng program ncreases total channel s proft and s Paretomprovng. Note that Pareto-mprovement may requre a sde-payment scheme from one

14 Les Cahers du GERAD G player to another. The dfferences n profts for retaler P ) C P ), manufacturer P ) C P ) and total channel P ch ) C P ch ) are gven by: P ) C P = 1 {[ M 4w M3 θ 1 γ) ] [ 2m 1 γ 1 θ)) M + M3 θ 1 γ) ] 2γ [ M 1 θ) + M 3 θ ] [ 2m 1 γ 1 θ)) M 3 P ) C P = 1 8w + M 3 3 θ 1 γ) ]}, { [2m 1 γ 1 θ)) M + M3 θ 1 γ) ] 2 = 1, 2. 9) 4m θ [ 2m 3 1 γ 1 θ)) M 3 + M θ 1 γ) ]}, = 1, 2. 10) P ch ) C P ch = [ P ) C P ] + [P ) C P ],, = 1, 2. 11) As t s notceable, these dfferences nvolve the nne parameters of the model margns and substtuton rates). From the above expressons, the proftablty of the coop plan can be derved only by statng suffcency condtons, one for each player, wthout ganng much analytcal nsght. Actually, unless one makes a long seres of assumptons regardng the relatonshps between the dfferent margns, t wll be extremely hard to tell f these condtons do actually ntersect or not. Our strategy to assess proftablty and hence mplementablty) of coop programs s to study some specal stuatons to get some addtonal hnts from results and then state conectures for the general case. The scenaros examned n detals are the followng ones: Symmetrc manufacturers and symmetrc retalers, Competng brands but no spatal competton,.e. γ = 0, Spatal competton between retalers and ndependent brands,.e. θ = Effcency n a Symmetrc Channel The assumpton here s that the two manufacturers and the two retalers are dentcal,.e. M = M, m = m,, = 1, 2. From 5)-6)-7)-11)-10) and 9), we get easly the followng marketng efforts, partcpaton rates and profts:

15 Les Cahers du GERAD G E ) C = E C = D = D = E = E = M [1 θ 1 γ)],, = 1, 2. 12) w 2m [1 γ 1 θ)] + M [1 θ 1 γ)],, = 1, 2. 13) 2w 2m [1 γ 1 θ)] M [1 θ 1 γ)],, = 1, 2. 14) 2m [1 γ 1 θ)] + M [1 θ 1 γ)] P ) C P = M [1 θ 2γ + θγ] [ E C E ], = 1, 2. 15) P ) C P = 1 2 [2m 1 2θ γ + θγ) M 1 θ + θγ)] [ E C E ], = 1, 2. 16) P ch ) C P ch = [2m 1 γ 2θ + θγ) + M 1 θ 4γ + θγ)] [ E C E ]. 17) Snce t s the manufacturer who s offerng the support, t makes sense to assume that a necessary condton for the mplementaton of a coop advertsng program s to be proft mprovng for hm. Ths condton becomes suffcent f t suts the retaler. The followng proposton shows that coop programs cannot be mplemented for a certan combnaton of brand and store substtuton rates. Proposton 6 If θ > 1 γ 2 γ, then both manufacturers wll not offer a coop support to retalers. Proof. From 16), t s easy to check that manufacturer, = 1, 2, ncreases hs proft wth a coop advertsng program f P ) C P > 0 2m M > 1 θ+θγ) 1 2θ γ+θγ), f 1 2θ γ + θγ) > 0 < 1 θ+θγ) 1 2θ γ+θγ), f 1 2θ γ + θγ) < 0 2m M > 1 θ+θγ) 1 2θ γ+θγ), < 1 θ+θγ) 1 2θ γ+θγ), 1 γ f θ < 2 γ 1 γ f θ > 2 γ. Snce by defnton the margns are postve, we conclude that f θ > 1 γ 2 γ, then P ) C P < 0.

16 Les Cahers du GERAD G Ths proposton says that f the brand substtuton rate s too hgh, then none of the manufacturers wll fnd t optmal to support hs retalers. Note that the hgher s the level of store competton, the narrower s the nterval for θ on whch the condton could be satsfed. 6 Further, the proftablty of the cooperatve program for manufacturers could be stated equvalently n terms of store substtuton,.e. γ > 1 2θ) 1 θ) or as a combnaton of the two,.e. 2θ γθ + γ > 1. Recall that under symmetry, the two manufacturers are dentcal and hence what holds true for one of them s also true for the other. We now take a closer look at the condton under whch coop advertsng programs would mprove profts of manufacturers, that s P ) C P > 0 2m M > fθ, γ) 18) where fθ, γ) = 1 θ + θγ) 1 2θ γ + θγ) and θ < 1 γ 2 γ. From the above condton, we conclude that n absence of store and brand competton, the cooperatve program s proftable for each manufacturer only f hs margn s hgher than half the retaler s margn 2m > M). A smlar condton was found n Jørgensen and al. 2000) for a one manufacturer one retaler channel s structure. Hence, under a compettve settng, we need a strnger condton on manufacturer s relatve margn to ensure the proftablty of the coop plan. Indeed, the condton s now 2m > Mfθ, γ) where fθ, γ) > 1 and t s harder to satsfy as store and/or brand competton ntensfy. 7 Even f the coop program s proft mprovng for manufacturers, t cannot be mplemented n the channel unless t s accepted by retalers. Hence, we look now at the problem from the retalers perspectve and provde the necessary condtons for a proftable mplementaton of the coop plan at ther level. 6 Indeed, t suffces to note that d dγ 1 γ 2 γ 1 = 2 γ) 2 < 0. 7 It s easy to check that fθ, γ) satsfes the followng propertes for θ < 1 γ 2 γ and 0 γ 1/2 fθ, γ) θ fθ, γ) γ = = 1 + γ γ 2 1 2θ γ + θγ) 2 > 0, 1 θ θ 2 1 2θ γ + θγ) 2 > 0, f0, 0) = 1, f0, γ) = 1 1 θ, fθ, 0) = 1 γ 1 2θ.

17 Les Cahers du GERAD G Proposton 7 Retaler, = 1, 2, wll mplement a coop advertsng program f θ < 1 2γ 1 γ. Proof. From 15), t s clear that P ) C P > 0 [1 θ 2γ + θγ] > 0, = 1, 2. θ < 1 2γ 1 γ. At the retalng level, the feasblty of a coop program requres also relatve low levels of brand competton. A more ntutve result could be derved from the alternatve condton on the store substtutablty rate obtaned equvalently from the above proposton.e. γ < 1 θ 2 θ. Therefore, retalers wll proft from the coop program mplementaton only when competton from the other store s not too hgh and ths condton gets strnger wth hgher substtutablty between brands. Puttng together the condtons derved for the proft mprovement at both the manufacturng and retalng levels, we get the followng { 2m M > 1 θ + θγ) 1 2γ 1 2θ γ + θγ), θ < mn 1 γ, 1 γ }. 19) 2 γ whch s equvalent to the followng result 2m M > 1 θ + θγ) 1 2θ γ + θγ), θ < 1 γ 2 γ, for γ 1 2γ, 1 γ for γ 0, ) 3 5 2, 1 2 An equvalent condton can be obtaned replacng θ by γ n the above expressons 8. To recaptulate, under full symmetry a cooperatve advertsng program s mplementable for low levels of brand and store substtuton rates. When competton at one or both channel levels s too hgh, the cooperatve program can be harmful for channel members although t wll ncrease marketng efforts. We have shown n the general case that total demand ncreases under coop advertsng program. In the symmetrc case, we have the stronger followng result statng that sales of each product n each outlet ncrease f such program s mplemented. 8 Defne by ). gγ) = 1 2γ 1 γ 1 γ 2 γ = γ 2 3γ γ) 2 γ). It s easy to check that gγ) > 0 for γ 0,

18 Les Cahers du GERAD G Proposton 8 If a coop advertsng program s mplemented, then Q ) C Q > 0,, = 1, 2. Proof. From 13), 12) and 1), one easly gets Q ) C Q = [1 γ θ + θγ] [ E C E ],, = 1, 2. whch s postve by the assumpton n 2). An obvous mplcaton of the above proposton s that demand rate n each store and for each manufacturer s brand also ncreases. 4.2 Effcency n Absence of Spatal Competton Ths scenaro consders a stuaton where the stores operate n non-overlappng terrtores γ = 0) but manufacturers brands stll compete n each retaler s outlet. The brand substtutablty stll can assume any feasble value,.e. θ [0, 1/2]. The demand rate s now ndependent of the competng retaler s marketng efforts and s gven by Q = 1 + E θe 3,, = 1, 2. 20) The optmzaton problems of retalers and manufacturers read max P = E,E 3 [ M 1 + E θe3 ) ) 1/2w 1 D E ) 2], = 1, 2. max D,D3 P = [ m 1 + E θe3 ) 1/2wD E) 2], = 1, 2. Each retaler s optmzaton problem s now one of a spatal monopolst sellng an assortment of competng products. As prevously, when coop programs are not offered, manufacturers are passve players and ther profts are obtaned smply by nsertng the equlbrum retalers marketng efforts strateges gven from 5) by E = M M 3 θ,, = 1, 2. w In the case where coop programs are offered and assumng an nteror soluton, the equlbrum marketng efforts and partcpaton rates strateges become from 6), 7)): ] ) E C 2m + [M M 3 θ =,, = 1, 2. 2w ] 2m [M D M 3 θ = ],, = 1, 2. 2m + [M M 3 θ

19 Les Cahers du GERAD G The nterpretaton of these strateges s very much smlar to the general case wth the dfference that they do not nvolve now any store competton ssue. The followng proposton characterzes the condtons under whch a coop program s effcent. Proposton 9 In the absence of spatal competton: ) a suffcent condton for manufacturer, = 1, 2, to mplement a coop advertsng program n retaler s, = 1, 2, outlet s ) Proof. ) 4m 2 4m [ 2θm3 2θM θ 2 )M ] + M θm 3 ) 2 > 0 f offered, retaler, = 1, 2, wll mplement the coop program θ. Use 10) to compute P ) C P = 1 8w { [2m M + θm3 ] 2 from whch one obtans easly the stated condton. ) Use 9) to compute P ) C P = 1 4w 4θm [ 2m3 M 3 + θm ]}, = 1, 2. [ M θm3 ] [ 2m M + θm3 ], = 1, 2. The curly bracket terms correspond to the numerator of E and E ) C whch are assumed nonnegatve. The man result establshed here s that n absence of a competton threat from another store, the retaler s always nterested by a coop program rrespectve of the competton ntensty between manufacturers. The coop plan proftablty for each manufacturer depends on a condton nvolvng hs margn, competng manufacturer s and retalers margns as well as the brand substtuton parameter. Note that ths condton s stated for each manufacturer s proftablty at each outlet, and s then suffcent but not necessary for the mplementaton of the coop program. Compared to the results known n a dyad marketng channel, we see here that a coop plan s not necessarly always proftable. Further, the above condton can be wrtten equvalently as m > ] 2 1/2wD [E )C ) C ),, = 1, 2. 21) Q Q

20 Les Cahers du GERAD G The numerator s the total cost of the coop program pad by manufacturer to retaler and the denomnator s the dfference n quanttes sold of brand wth and wthout a coop plan. Therefore, f manufacturer s margn s greater than the per unt cost of ncremental sales then the program s proftable for hm. Ths s farly ntutve. The mplct assumpton when statng the condton n 21) s that the soluton of the equlbrum problem wth support s nteror.e., D > 0). The denomnator s nonnegatve f Q ) C Q = [ E ) ] [ C E E ) ] C θ 3 E 3 > 0,, = 1, 2. whch s equvalent to θ < [ ) ] C E E [ ) C ],, = 1, 2. 22) E3 E 3 The above condton shows that the rato of ncremental marketng efforts n the same outlet for the competng brands should be greater than the substtuton rate. If t was not the case, the manufacturer wll not support the retaler. Note that n absence of store competton, category sales n each outlet ncreases and hence grand total sales. Indeed, ncremental category sales are now gven by [ Q ) ] C Q = [ E ) ] C [1 θ] E, = 1, 2. whch s clearly postve. 4.3 Effcency n Absence of Brand Competton We turn now to the case where retalers have overlappng terrtores. The two brands are not n competton whch amounts to say that they are desgnated to two dfferent market segments or pertan to ndependent product categores. Equlbra and proft functons for ths scenaro are obtaned by settng to zero the brand substtutablty parameter n the orgnal model θ = 0). The demand rates are now Q = 1 + E γe 3,, = 1, 2. 23) The optmzaton problems of channel members read max P = [ ) M E 1 + E γe 3 1/2w 1 D) E ) 2],,E 3 =1,2 = 1, 2. 24) max P = ) [m 1 + E γe 3 1/2wDE ) 2], = 1, 2. 25) D,D3 =1,2

21 Les Cahers du GERAD G From 5), 6)and 7) one gets the equlbrum strateges: E = M,, = 1, 2. w ) E C 2m 1 γ) + M =,, = 1, 2. 2w D = 2m 1 γ) M 2m 1 γ) + M,, = 1, 2. Although the nterpretaton of these strateges are very much smlar to the ones obtaned n the general case, one must stress that the support rate provded by manufacturer s ndependent of hs compettor s actons. Ths stuaton s then equvalent to a monopolstc manufacturer dstrbutng hs product n two competng stores. Retaler s marketng effort decson on brand s also ndependent of her decson regardng the competng brand. Proposton 10 In absence of brand competton, ) Manufacturers wll offer a coop support γ. ) a suffcent condton for retaler, = 1, 2, to mplement a coop advertsng program for brand, = 1, 2, s [ ] M < 2 1 γ) 1 2γ) m + γm 3. Proof. ) Use 9) to compute P ) C P = 1 4w M and hence the stated condton. ) Use 10) to compute [ P ) C P = 1 8w whch s clearly postve γ. 2 1 γ) 1 2γ) m M + 2γM 3 [ 2 1 γ) m M ] 2, = 1, 2. ], = 1, 2. The above result shows that the cooperatve plan s always benefcal for a manufacturer when hs product does not face competton n the same outlet. To be benefcal for a retaler, a condton relatng margns and store substtuton rate must be satsfed. From 9), n absence of brand substtutablty, the retaler ncreases her proft for each

22 Les Cahers du GERAD G brand only when the followng condton on marketng efforts and store competton s satsfed 9 [ ) ] C E E [ ) ] C > 2γ,, = 1, 2. E 3 E 3 The rato of ncremental marketng effort for the same brand n competng outlets should be twce greater than the store substtuton rate. Ths clearly shows that the effcency of such programs s not always guaranteed for the retalers. The effect of cooperatve advertsng n one manufacturer multple retalers channel has been nvestgated by Bergen and John 1997) who obtaned a dfferent result. The authors found that a coop advertsng plan along wth a two-part tarff wholesale prcng program can be an effcent tool to reach the vertcally ntegrated channel profts level. In terms of sales, when θ = 0, we have the followng ncremental demands ) [ Q C Q E ) ] [ ) ] C C = E γ E 3 E 3,, = 1, 2. [ Q ) ] C Q = { [E ) ] [ ) ]} C C E γ E 3 E 3, = 1, 2. [ Q ) ] C Q = [ E ) ] C [1 γ] E, = 1, 2. [ ) ]) C Clearly, each manufacturer sales Q Q are hgher when he offers a coop ) program to hs dealers. Demand for product n outlet Q,, = 1, 2 ncreases f [ ) ] C E E [ E 3 ) C E 3 9 In the general model, The retaler s profts n 9 could also be wrtten ] > γ,, = 1, 2. 26) P C P = 1 2 2γ [ ] M M3 θ 1 γ) [ ] M 1 θ) + M3 θ E E 3 C E, = 1, 2. C E 3 For θ = 0, the above dfference becomes P C P = 1 2 M E C E 2γ E 3 C E 3, = 1, 2.

23 Les Cahers du GERAD G that s the rato of ncremental marketng efforts by the retalers s lower than the store substtuton rate. Ths result mrrors the one obtaned n the prevous scenaro: absence of spatal competton and presence of brand competton see 22)). 5 Implcatons of Fndngs and Conclusons Are cooperatve advertsng programs coordnatng mechansms n compettve channels? For who s t benefcal and under whch condtons? Ths paper provdes a novel answer to these questons. Prevous studes establshed the effcency of such programs to enhance marketng efforts and total channel profts n two-member channels. In realstc settngs, outlets and manufacturers are however faced wth competton from smlar nsttutons. We nvestgate whether prevous fndngs for dyad channels stll hold when competton s consdered at the store and/or the brand levels. Our model provdes helpful nsghts nto the analyss of channel structures composed of multple retalers and manufacturers and accounts for drect and cross-competton effects between brands and stores. Our results valdate prevous fndngs n the cooperatve advertsng lterature for blateral monopoles and demonstrate that coop plans are effcent tools to coordnate the channel when no competton s present at both levels. For compettve channels, the coop plan ncreases marketng efforts and s benefcal to fnal consumers. However, retalers and manufacturers do not necessarly beneft from the cooperatve plan n all market condtons. We show ndeed that the effcency of the cooperatve advertsng program s not always guaranteed for those channel members who are facng competton unless certan condtons on store and brand substtutablty as well as on margns are verfed. Hence, when competng products are dstrbuted through outlets located n non-overlappng terrtores, the cooperatve program mproves each retaler s proft and demand rate but s not always benefcal for manufacturers. Further, n a market structure characterzed by competng stores sellng hghly dfferentated products, the mplementaton of the coop plan s benefcal to each manufacturer s proft and demand rate. However, a retaler would beneft from such a plan only f her marketng efforts for the brand are suffcently hgh compared to her competng store s efforts. An mportant mplcaton of ths fndng s that monopolstc manufacturers and/or retalers should revse the effcency of the coop plan after the entry of a new compettor n the market. In a marketplace where competton s present at both channel levels, and assumng symmetrc margns, manufacturers would offer the cooperatve program and retalers would agree for t only for low levels of store and brand substtuton rates. Hence, n hghly compettve markets, cooperatve advertsng could generate destructve compettve effects that would harm channel members benefts, although t would stll be benefcal for consumers. Manufacturers wll ncrease ther coop support to retalers as brand competton gets more ntense. However, they should offer less coop rates as stores become more substtutable. Agan, channel members should consder carefully substtuton rates n ther market and revew the cooperatve plan agreement when competton at the store and/or the brand levels get ntensfed.

24 Les Cahers du GERAD G Despte these mportant manageral mplcatons, our results have some lmtatons related to the smplfyng assumptons of the model. In our setup, we assumed that advertsng effcency and baselne sales are equal n all stores. Each retaler could ncrease both effects by mprovng her advertsng effcency and engagng n advertsng actvtes for the store. It would be partcularly nterestng as a future research to nvestgate whether levels of advertsng effcency n competng stores can nfluence the effcency of the cooperatve plan. A further lmtaton of our model s that we assumed fxed prces. Although ths assumpton permts to derve analytcal results, varyng retal and transfer prces n the orgnal model would yeld helpful nsght to set condtons for the effcency of the coop plan, especally by specfyng the relatons between margns and store and brand competton ntensty. Our model could also be enrched by consderng endogenous substtutablty parameters. The product substtutablty parameter can be modelled as a functon of manufacturer s advertsng levels rather than as an exogenous parameter as suggested n Bergen and John 1997). The store substtutablty effect could vary wth the retalers advertsng levels for ther outlets. Fnally, further work on ths topc could also nclude dfferent forms of demand functons, carry-over effects of advertsng actvtes and dfferent forms of channel competton. The emergence of the e-commerce and the retalers prvate labels create ndeed vertcal competton between retalers and manufacturers. Appendx: Proof of Proposton 2 We frst solve retaler s problem max P = E,E 3 2 =1 { [ M 1 + E γ 1 θ) E 3 1/2w 1 D ) E ) 2}, = 1, 2. ] θ 1 γ) E3 θγe3 3 Frst order condtons for retaler, = 1, 2, are obtaned by maxmzng the rght-handsde of the above expresson and are gven by P E = 0 M M 3 θ 1 γ) w 1 D ) E = 0, = 1, 2. whch leads to the followng reacton functons ) E C M M 3 θ 1 γ) = ),, = 1, 2. w 1 D

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