廣告與通路結構關係之探討

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(1)國立中山大學企業管理學系博士班博士論文. 廣告與通路結構關係之探討 Advertising and Channel Structures. 研究生：汪秩仁撰指導教授：吳基逞. 中華民國九十七年十二月.

(2) 誌謝經過博士班嚴格的訓練歷程，最終總算能完成本論文的寫作。首先，最感謝的當然是我的指導教授吳基逞老師，他總是不離不棄，從旁耐心地悉心教導，並指引我正確的思考方向。在此也特別感謝曾美君教授、邱郁秀教授、陳瀅儒教授、蕭櫓教授、黃明新教授擔任我的口試委員，給予我建設性的建議，由衷地感謝您們的用心，補足了本研究許多的缺失。在撰寫論文的過程中，我必須感謝許多人的幫助，讓我的論文能夠順利完成，感謝陳瀅儒教授在英文上的潤稿、文章結構上的調整、及許多問題上提供寶貴的修改建議，讓我的論文更為嚴謹順暢。此外，也感謝學弟妹在文獻搜尋上的協助。最後，把最特別的感謝獻給永遠支持我的家人，感謝您們不離不棄，在我心情不好時給我安慰、鼓勵，給我力量勇敢地面對挑戰，您們是我一輩子的依靠與驕傲！. 汪秩仁謹誌於西子灣 2008.11.28. I.

(3) 摘要廣告效應從 1920 年代開始至今就一直是研究的重要議題。例如在經濟領域、行銷領域上。經濟領域研究的焦點集中在對社會福利、消費者福利的影響；而行銷領域研究的焦點則集中在對消費者行為的影響、廠商間競爭性互動的影響。這些研究都集中在整合行銷通路的情境下來探討，然而只有到近幾年才有學者開始討論共同零售商通路的情境。在實務上，間接通路是極為普遍的，而在不同的通路結構中，由於零售商獨立的存在與所處特定的競爭情境，而使得廣告與通路結構間存在著互動的可能影響，因此本研究利用賽局理論進一步地探討通路結構與廣告這兩種策略性決策間值得進一步探討的三個議題。第一個議題探討廣告在不同通路結構中的策略性角色差異。本文主張廣告策略角色的使用受到通路結構相當大的影響。明確地說，本文闡述，相較於其他兩種通路結構，當製造商將銷售責任委與專屬的零售商時，製造商有更高的機率會藉由資訊性廣告的促成競爭本質來獲取更大的利潤。相反的，相較於專屬零售商通路，當製造商採取整合通路或共同零售商通路時，說服性廣告會被更廣泛地使用。本文可以提供一個理論基礎，從製造商與零售商間因廣告而產生的策略性互動中，從製造商的觀點來說明，這兩種廣告策略如何在不同的通路結構中成為廠商最適的選擇。因此而能提供製造商一個操作準則，用以決定在不同的通路情境中該如何運用廣告的策略性角色。第二個議題探討直接與間接通路的選擇問題。本文主張專屬零售商通路結構所提供的價格競爭緩衝機制，會在兩種情況下，即使是兩者的產品差異性很低，也會顯得微不足道，而使得整合的直接通路變得較為有利。第一種情況為，製造商擁有足夠多的忠誠顧客，雖然採用整合通路會因面對面的直接競爭而使價格下降，但這樣的低價反而能吸引足夠多的忠誠者購買。第二種情況為，即使忠誠顧客不夠多，但若考慮可能的廣告競爭，製造商仍然會傾向選擇整合通路，而比較不在意價格競爭的問題。此乃因採用間接. II.

(4) 通路會迫使製造商陷入廣告的囚犯困境，而虛擲更多的廣告花費。第三個議題探討說服性廣告在共同零售商通路結構中所產生的利益衝突問題。現行的行銷文獻認為說服性廣告往往會激起競爭對手的報復行動(投入更多的廣告)，或者激起共同零售商採取反制的做法(消極上推介沒有廣告的品牌，積極上引進私有品牌)。然而最近亦有實證研究發現，大多數並不會激起這些行動。其中一種可能是反制並不見得更為有利，但本文提出另一種可能是，也許策略性地使用說服性廣告除了自己可以獲利外，並不見得會傷害通路中的其他成員。本文將說服性廣告效果模型化為兩種效果，一方面廣告可以使消費者更喜歡自己的品牌(絕對效果)；另一方面，也會使競爭品牌更難取代(相對效果)。藉此，本文顯示只要製造商能策略性地選擇廣告要影響的對象，那麼通路衝突是可以避免的。相較於現今的文獻，本文的廣告策略乍看之下似乎會傷害其他成員，但卻可藉由聰明地選擇廣告目標閱聽眾，而可以使所有的通路成員，廣告的製造商自己、競爭對手、及共同零售商均獲益，以達柏拉圖改進，避免激起其它成員反制。. 關鍵詞：資訊性廣告, 說服性廣告, 通路結構, 產品替代性, 賽局理論。. III.

(5) Abstract Due to the important role of advertising in marketing practice, its effects have been the research focus since 1920. Among relevant research fields, the issue that has been paid close attention in the economic field is its impact on consumer welfare. Issues focused in the marketing field are its impacts on consumer perception, feelings, attitudes, behaviors, and competitive interaction among firms. However, in these two fields the integrated channel is the focused scenario where the advertising works in vast majority of literatures. Only very few of them investigate effects of advertising in other channel structure context. However, in practice indirect channels are very common. There may be interactions between advertising and channel structure due to the existence of the independent retailer and the specific degree of competition. Since advertising is an important strategic instrument, it deserves to pay more efforts to relate the advertising and channel structure. This dissertation use game-theoretical approach to target three issues relating the advertising and channel structure. The first issue focuses on discussing the differential of choices between informative and persuasive advertising across three channel structure contexts for two competing manufacturers. This dissertation argues that the use of advertising strategy crucially depends on the channel structure. Specifically, it shows that when manufacturers delegate the sales responsibility to dedicated retailers, informative advertising may yield a higher profit for the manufacturers due to its pro-competitive nature. On the contrary, persuasive advertising should be used more extensively when either the manufacturers sell directly to the end consumers or sell through a common retailer. This therefore provides a theoretical foundation for why both advertising strategies can emerge as optimal responses from the manufacturers' viewpoints and subsequently provides handy guidelines for when these advertising strategies should be used in various scenarios. The second issue is about the choice between direct and indirect channels. The introduction of independent retailers has long been recognized as a buffer that alleviates the price competition between channels. If the sales responsibility is delegated to the retailers, the retail prices are driven upwards, thereby allowing the manufacturers to avoid the head-to-head. IV.

(6) competition. In this dissertation, we argue that this effect may be counter-balanced if the manufacturers are privileged with sufficiently large loyal segments. It shows that, selling directly to the consumers (through the direct channel) may be more beneficial for the manufacturers than delegation with the presence of competition, because the low prices due to the intense competition may help the manufacturers to extract more revenue from loyal consumers. Furthermore, if the manufacturers compete along dimensions that differ from prices, they may be further in favor of the direct channel and less concerned about price competition. In particular, this dissertation shows that if the manufacturers also compete on their advertising strategies, delegating to the retailers may force them to invest on the wasteful advertising, which could be prevented had the manufacturers sold the products themselves. The third issue discusses the combativeness of the persuasive advertising in the common retailer channel. The existing marketing literature suggests that persuasive advertising elicits counteractions from competing manufacturers and consequently leads to wasteful cancellation of the advertising effects. However, recent empirical studies document a surprisingly negative result against this conventional wisdom. To provide a theoretical ground for this empirical puzzle, we propose a novel way to model the advertising effect on the consumers' preference that incorporates two critical driving forces: on one hand, advertising shifts the consumers' preferences towards the advertised product (the "absolute effect"); on the other hand, it also makes the rival product a less desirable substitute from the consumers' viewpoints (the "relative effect"). Through our alternative interpretation of persuasive advertising, we show that channel conflict can be alleviated if a manufacturer adopts persuasive advertising that wisely "targets" appropriate consumers. In stark contrast with the established work, this advertising strategy may give rise to profit increases for every channel member, including the rival manufacturer and the retailer that were previously believed to always counteract/ resist to such persuasive advertising. We further identify the detailed operating regimes within which such a manufacturer-initiated persuasive advertising strategy is no more harmful for other channel members.. Keywords: informative advertising, persuasive advertising, channel structure, product substitutability, game theory. V.

(7) Contents Chapter 1 Introduction........................................................................................1 Chapter 2 Strategic Roles of Advertising in Distribution Channels...................4 2.1 Introduction.........................................................................................................................4 2.2 The Model...........................................................................................................................8 2.3 Equilibrium Analysis........................................................................................................11 2.3.1 Advertising Equilibrium under Each Channel Structure………...............................11 2.3.2 Advertising Strategies and Channel Structure...........................................................16 2.3.3 Discussions………………………..………………………………….………….....21 2.4 Concluding Remarks.........................................................................................................21 Appendix………………………………………………………………………….…………22. Chapter 3 Channel Structures, Brand Loyalty, and Advertising......................32 3.1 Introduction.......................................................................................................................32 3.2 The Model.........................................................................................................................36 3.3 The Impact of Loyal Segments.........................................................................................39 3.4 Advertising Competition……….......................................................................................41 3.4.1 Direct Channel…………………...............................................................................42 3.4.2 Indirect Channel.........................................................................................................44. VI.

(8) 3.4.3 Channel Comparison………….. ...............................................................................45 3.5. Discussions and Conclusions………...............................................................................47 Appendix.................................................................................................................................48. Chapter 4 Is Persuasive Advertising Always Combative in a Distribution Channel?..........................................................................................58 4.1 Introduction.......................................................................................................................58 4.2 The Model.........................................................................................................................62 4.3 The Impact of Persuasive Advertising..............................................................................64 4.3.1 All Consumers Are Exposed......................................................................................65 4.3.2 Only Consumers with Moderate/Weak Preferences Are Exposed............................66 4.3.3 Only Consumers with Strong Preferences Are Exposed...........................................69 4.4 Discussions and Concluding Remarks………………………..……………....................70 Appendix………………………………………………………..…………….......................71. Chapter 5 Conclusions………………………...……….………...…..…………………...80 References………………………………......……………………………..………………..82. VII.

(9) Chapter 1 Introduction Due to the important role of advertising in marketing practice, its effects have been the research focus all the time. Among relevant research fields, the issue that has been paid close attention in the economic field is its impact on consumer welfare. It has been asserted that the informative advertising provides information, promotes competition, and thus increases consumer welfare; on the contrary, the persuasive advertising alters consumer preference, increases perceived product differentiation which is not real sometimes, alleviates competition, and thus decreases consumer welfare. On the stance of firms, they care their own profits more than consumer welfare. They would try their best to avoid competition. Therefore, researchers (Dixit and Norman 1978, Stegeman 1991, Stahl 1994) claim that the informative advertising is always too less but the persuasive one is always too much. Issues focused in the marketing field are its impacts on consumer perception, feelings, attitudes, behaviors, and competitive interaction among firms. However, in these two fields the integrated channel is the focused scenario where the advertising works in vast majority of literatures. Only very few of them investigate effects of advertising in other channel structure context, not to mention to compare the working differentials of advertising across different channel structures. However, in practice indirect channels are very common. There are various forms of indirect channel structures, e.g., dedicated retailer channel, monopoly common retailer channel, duopoly common retailer channel, hybrid channel, etc. Manufactures would act in different patterns across channel structures because one channel structure constructs a specific degree of competition. Since advertising is an important strategic instrument, it deserves to pay more efforts to relate the advertising and channel structure. The dissertation would target three issues relating the advertising and channel structures. The first issue focuses on discussing the differential of choices between informative and persuasive advertising across three channel structure contexts for two competing manufacturers. The second issue is about the proposition that intermediaries may reduce price competition among manufacturers, which increases their profits, and thus manufacturers prefer indirect dedicated retailers to direct channels when competition is intense. We examine whether it is also valid when we consider both price and advertising competition between two manufacturers with loyal consumers. The third issue is about the profit of individual 1.

(10) channel member in the common retailer system impacted by the persuasive advertising. We check whether it is possible to find out certain conditions where the persuasive advertising may not harm any channel member. By discussing on the first issue, we can understand whether the probability of observing informative advertising in equilibrium is all the same across three channel structures, the integrated channel structure, the dedicated retailer structure, and the common retailer structure. Is it possible that manufacturers would adopt informative advertising rather than persuasive one more probably in a certain channel structure? What are the conditions? And is it likely that on certain conditions manufacturers would adopt informative advertising in one channel structure but otherwise in another channel structure? By identifying operating conditions under which one form of advertising strategy is more favorable than the other in each specific channel structure, we can thereby provide a handy guideline for practitioners to design their advertising strategically. The second issue discusses the validity of the proposition that dedicated intermediaries can mitigate price competition between manufacturers. Is it possible that manufacturers with integrated channel structures can be better off than those with dedicated retailers although dedicated retailers can work as buffers between manufacturers when their products are less differentiated? What will happen to these two channel systems if we introduce both price and advertising competition with loyal consumers? This would give us more insight into the choice of channel structure because the multi-competition dimensions and the privilege of loyal consumers are very common in practices. Finally the dissertation switches the focus from integrated channel systems and dedicated retailer systems to the common retailer system in the third issue. Trying to explore impacts of the persuasive advertising on channel members in an alternative way, I would like to find out conditions in which persuasive advertising that decreases the manufacturer’s product substitutability can relax its combative nature and lead to no channel conflict without the advertising manufacturer’s suffering losing profit. The dissertation academically contributes to first explore two primary effects of advertising across channel structures. It let us look into the differential working of advertising across channel structures more delicately. This would advise us that researchers should 2.

(11) be more careful when they draw conclusions about advertising from a specific distribution channel. We may no longer regard the advertising competition as the same across different channel structures. Under the same inherent product differentiation, persuasive advertising may be prevalent in certain channel structure, while informative one may be prevalent in other channel structure. Additionally, after incorporating advertising effects into price competition, the dissertation discloses conditions where the integrated channel structure is more beneficial than the dedicated channel structure. This would complement the claim that each manufacturer will distribute its product through dedicated channel for highly competitive goods. Furthermore, the dissertation also contributes to propose remedies for the weakness in Shaffer and Zettelmeyer (2004a). They find conditions where channel conflict in the common retailer channel need not arise. However, all channel members get worse due to a manufacturer’s persuasive advertising under such conditions. For marketing managers, they can have a clearer picture about advertising competition across different channel structures and may not miss to engage in an inappropriate advertising campaign given their channel structure contexts.. 3.

(12) Chapter 2 Strategic Roles of Advertising in Distribution Channels 2.1. Introduction. The impact of advertising on price, price sensitivity, or competition has been a long-standing issue in the marketing and economic literature. Researchers typically classify the advertising strategies into two categories. “Informative advertising” shifts the consumers’ preferences about product attributes and terms of sale uniformly towards both the advertised product and its close substitutes, thereby leading to pro-competitive consequences (Stigler (1961)). On the contrary, “persuasive advertising” shifts the consumers’ preferences towards the advertised product and at the same time makes the rival product a less desirable substitute from the consumers’ viewpoints (see, e.g., Braithwaite (1928) and Tirole (1988)). This implies that persuasive advertising enhances product differentiation and consequently is typically perceived as anti-competitive (Bain (1956) and von der Fehr and Stevik (1998)). These two opposite effects suggest that the advertising strategies of the marketing managers should be used to strategically adjust the appropriate competition intensity in different situations. These two strategic roles of the advertising have been discussed in the economics/ marketing literature. For example, Wernerfelt (1985) relates these two roles to the product life cycle and the firm size. Meurer and Stahl (1994), Soberman (2004), and von der Fehr and Stevik (1998) investigate the effect of adopting different advertising strategies in response to the inherent level of product differentiation. They show that when the level of inherent differentiation is high (low), firms may intend to use informative advertising (persuasive advertising). Parker and Kim (1999) argue that persuasive advertising may allow national brands to enhance product differentiation and avoid the cannibalization issue with the private labels. See Bagwell (2007) for a comprehensive and recent survey of papers that contribute to the understanding of these strategic roles. The aforementioned work, however, does not take into account the possibility of selling through an indirect channel, which has been a pervasive business practice nowadays. For example, automobile manufacturers sell their cars through dedicated retailers with exclusive 4.

(13) territories (Ingene and Parry (1995)). Apparels, consumer electronics, home appliances, and etc. are typically sold through retailers such as Costco, Home Depot, Wal-Mart and others (Schiller and Zellner (1992)). The indirect channels are particularly common or even essential for global supply chains; e.g., Costco exports various products from the US that are unavailable in other outlets in other countries. Stemming from the seminal paper by McGuire and Staelin (1983), it has been well acknowledged that an individual firm (manufacturer hereafter) would strategically behave differently across different channel structures in accordance with specific competition status; see also Bernheim and Whinston (1985), Bonanno and Vickers (1988), Coughlan (1985), Gupta and Loulou (1998), Moorthy (1988), and Rey and Stiglitz (1995). A conventional wisdom from this research stream is that the choice of channel structure crucially depends on the level of product differentiation: manufacturers may prefer selling through independent (and dedicated) retailers if the products are highly substitutable, but are better off by selling directly to the consumers with sufficient product differentiation. To the best of our knowledge, the discussions of using different advertising strategies in the indirect channel focus exclusively on the common retail channel. These include Shaffer and Zettelmeyer (2002, 2004a,b), who explore the impacts of manufacturer’s persuasive advertising in the common retail channel, and Sethuraman and Tellis (2002), who address how the common retailer’s price promotion is affected by the manufacturers’ advertising strategies. This chapter attempts to provide a unified framework towards a thorough understanding of the interplay between the advertising strategies and the channel structure. Specifically, we argue that the use of advertising strategy crucially depends on the channel structure, because the channel structure drives the nature of “competition” between the manufacturers. Consequently either the pro-competitive (informative) role or anti-competitive function (persuasive) role of advertising may be optimal. This previously ignored connection appears to be very natural in various practical scenarios; further, we are able to identify operating regions under which one form of advertising strategy is more favorable than the other, thereby providing a handy guideline for practitioners to design their advertising strategically. To illustrate our ideas, we construct a stylized model in which two manufacturers sell. 5.

(14) horizontally differentiated products and can choose between two advertising strategies (persuasive or informative) exclusively. Consumers are price sensitive, and their preferences will be affected by the advertising of the manufacturers. In this chapter, advertising may enable a manufacturer either to create more perceived product differentiation (through persuasive advertising), or to provide information about brand attributes and expand the market base of consumers who are well aware of his product (through informative advertising). Each manufacturer can either choose informative advertising, persuasive advertising, or simply no advertising. The exclusive nature of these advertising strategies is intended to capture the resource constraint a manufacturer may face in the advertising expenditure. To investigate the roles of advertising strategies and their consequences, we consider three channel structures: 1) the integrated channel in which both manufacturers sell the products directly to the consumers; 2) the delegated channel in which both manufacturers delegate the sales responsibility to the dedicated retailers; and 3) the common retailer channel in which both manufacturers sell their products through a common (independent) retailer. We use the wholesale price contracts to specify the transactions between the manufacturers and the retailer(s). We show that informative advertising is most likely to emerge as an equilibrium outcome in the delegated channel, followed by the integrated and common retailer channels, in descending order. To understand this result, let us first start with the delegated channel. From McGuire and Staelin (1983), in a delegated channel, the independent retailers intend to mark up the prices to claim their profits, thereby driving up the retail prices. On one hand, this “buffering” mitigates the intense price competition between channels; on the other hand, it also results in excessively low demand that could ultimately hurt the manufacturers. From the manufacturers’ perspective, a remedy to this unfavorable consequence is therefore to invest in informative advertising to increase the level of competition between retailers. This induces the retailers to set a lower retail price, thereby boosting the demand from the consumers. We thus are able to identify the regions in which informative advertising is adopted despite the seeming dominance of persuasive advertising. The above argument shows that the retailer buffer promotes informative advertising.. 6.

(15) However, when both manufacturers sell through a common retailer, things are dramatically different. As the common retailer behaves as a monopolist while facing all three groups of the consumers, she is more concerned about the effective demand while determining the retail prices (compared to the manufacturers). Consequently, when the manufacturers adopt persuasive advertising and increase the wholesale prices, the common retailer optimally responds by reducing the retail margins to mitigate this price effect. This in turn strengthens the manufacturers’ incentive of adopting persuasive advertising (over informative advertising), for the benefit from the enhanced product differentiation is entirely captured by the manufacturers rather than the common retailer. Our results suggest that the nature of the competition in the downstream consequently affects the upstream manufacturers’ strategic concerns of adopting their advertising strategies. As aforementioned, our work is related to vast literature that elaborates the strategic role of different advertising strategies. Unlike our work that considers the possibility of selling through indirect channels, most of the established work is confined within the direct channel framework, including Dixit and Norman (1978), Meurer and Stahl (1994), Parker and Kim (1999), Singh et al. (1998), Soberman (2004), Stegeman (1991), and von der Fehr and Stevik (1998). Under this channel structure, it is not surprising that persuasive advertising is more favorable from the manufacturers’ viewpoints because it enhances product differentiation. Our results compensate this research stream by linking the channel structure to the manufacturers’ incentive of offering informative/ persuasive advertising, and highlight the strategic interactions along the distribution channel. The advertising strategies in the common retailer channel settings have been investigated in Shaffer and Zettelmeyer (2002, 2004a,b), and Sethuraman and Tellis (2002). Shaffer and Zettelmeyer (2002, 2004a,b) focus exclusively on the persuasive advertising and investigate the benefit of using targeted advertising to create product differentiation. Moreover, they adopt a bargaining framework to describe how the channel profit is shared among the manufacturers and retailers. In contrast, we study both the informative and persuasive advertising strategies, and we allow the manufacturers to sell through dedicated retailers as well. In addition, we model the pricing games between the manufacturers and the retailers, which enables. 7.

(16) us to explicitly present the strategic interaction along and across the distribution channels. Sethuraman and Tellis (2002) suggest that informative advertising can stimulate the common retailer’s price promotion due to the enhanced product competition, but persuasive advertising discourages price promotion. This chapter addresses different issues, and we also study the advertising strategies when the manufacturers sell through dedicated retailers. The rest of this chapter is organized as follows. We discuss our model characteristics in Section 2.2. In Section 2.3, we analyze and compare the equilibrium outcomes advertising strategies in different channel structures. Section 2.4 provides some concluding remarks. All the proofs are relegated to the appendix.. 2.2. The Model. We consider a distribution channel in which two manufacturers M1 and M2 intend to sell horizontally differentiated products (denoted by m1 and m2 ) to the consumers. The manufacturers’ production costs are assumed to be symmetric, and are normalized to zero without loss of generality. Consumers are price sensitive, and their preferences will be affected by the advertising of the manufacturers. In this chapter, advertising may enable a manufacturer either to create more perceived product differentiation (through persuasive advertising), or to provide information about brand attributes and expand the market base of consumers who are well aware of his product (through informative advertising). To explicitly model the strategic effect of these advertising strategies, we classify the consumers into three groups, G1 , G2 , and Gc . The group Gi (i = 1, 2) comprises consumers that are familiar with (aware of) mi but are unaware of mj . We label these groups of consumers the “local consumers” of these two manufacturers, respectively. On the contrary, Gc comprises consumers who are aware of both products m1 and m2 . Let us first ignore the effect of informative advertising. Given the prices pi and pj of products mi and mj , the consumers’ purchasing behaviors are as follows. In group Gi , each consumer purchases mi with probability 1 −pi and walk away left-handed otherwise; these consumers never purchase the other product since they are unaware of it. On the contrary, each consumer in group 8.

(17) Gc purchases mi (mj ) with probability 12 [1 − pi + θ (pj − pi )] ( 12 [1 − pj + θ (pi − pj )] ), where θ ≥ 0 represents the degree of inherent product differentiation. As θ becomes larger, the substitutability between the two products gets higher and consequently the competition is more intense. Since the manufacturers are able to make informative advertising to make some unaware consumers become aware of their products, the (final) sizes/populations of these groups depend on manufacturer’s informative advertising strategy. Initially, we assume that, after normalization, the sizes of groups G1 , G2 , and Gc are 1, 1, and 2β, respectively. The parameter β allows us to adjust the relative size of those consumers that have been aware of both products initially (compared to those unaware consumers). As an example, if only Mj makes informative advertising, all consumers originally in group Gi will become aware of product mj ; consequently, the populations of group Gi , Gj , and Gc will be 0, 1, and 1 + 2β, respectively. In such a scenario, the effective demand for mi is 1 [1 − pi + θ (pj − pi )](1 + 2β), 2 where 12 [1 − pi + θ (pj − pi )] corresponds to the probability that a consumer in group Gc purchases mi and 1 + 2β is the population of this group. Likewise, the demand for mj is 1 (1 − pj ) · 1 + [1 − pj + θ (pi − pj )](1 + 2β), 2 where, in addition to the purchases from group Gc , the consumers in group Gj also purchase with probability 1−pj . As another example, if both Mi and Mj make informative advertising, all consumers fall into group Gc . In this case, the demands for mi and mj are 12 [1 − pi + θ (pj − pi )](2 + 2β) and 12 [1 − pj + θ (pi − pj )](2 + 2β), respectively. Now we introduce the effect of persuasive advertising. Since these consumers in G1 and G2 are mainly unaware of the rival’s product, persuasive advertising has no impact on their preferences; therefore, persuasive advertising does not affect the aggregate demand in these groups. However, the purchasing behaviors of those consumers in group Gc are significantly altered by persuasive advertising. This is modeled by reducing the impact of pj on mi ’s and mj ’s demand if Mj engages in persuasive advertising. Specifically, after taking persuasive advertising into consideration, for the consumers in groups Gc , the possibility of choosing 9.

(18) mi (mj ) is 12 [1 − pi + θ (γj pj − γi pi )] ( 12 [1 − pj + θ (γi pi − γj pj )]),where γi = γ (γ j = γ) if Mi (Mj ) engages in persuasive advertising, and γi = 1 otherwise. The parameter γ ∈ [0, 1) captures the effect of persuasive advertising: when γ decreases, persuasive advertising shifts the consumers’ demand more effectively. Collectively, the aggregate demand for mi sums up the demands from Gi , Gc , and Gj , and can be represented as by the following inverse demand function (cf. Choi (1996)): φi + φj φi − φj )(1 − pi ) + β + θ (γj pj − γi pi ) , (1) qi = (1 + β + 2 2 where φi. γi.   0 if M does not engage in informative ads, i =  1 if Mi engages in informative ads,   1 if M does not engage in persuasive ads, i =  γ if Mi engages in persuasive ads.. We assume that each manufacturer can either choose informative advertising, persuasive advertising, or simply no advertising. The exclusive nature of these advertising strategies is intended to capture the resource constraint a manufacturer may face in the advertising expenditure. It also allows us to isolate the manufacturers’ rationale of using these alternative advertising strategies. To highlight the effect of these advertising strategies, we normalize the production costs, retailer processing costs, and advertising costs to zero without loss of generality. Our primary goal is to demonstrate the strategic roles of advertising in different channel structures. To this end, we consider three channel structures: 1) the integrated channel, 2) the delegated channel, and 3) the common retailer channel. In the integrated channel, both manufacturers sell their products directly to final consumers. In the delegated channel context, each manufacturer sells his product through an independent, dedicated retailer. In the common retailer channel, both manufacturers must sell their products through this common retailer. These different channel structures also lead to different sequences of events. In the integrated channel, both manufacturers first simultaneously decide advertising strategies, and 10.

(19) then simultaneously set prices for consumers. In the delegated channel, both manufacturers simultaneously decide advertising strategies; after the advertising strategies are made public, they simultaneously set the wholesale prices for retailers; finally, each retailer simultaneously determines the price for consumers. In the common retailer channel, both manufacturers simultaneously decide advertising strategies; after the advertising strategies are made public, they then simultaneously set the wholesale prices; finally, the common retailer sets prices for consumers given these wholesale prices. Since the game involves multiple stages of strategic interactions, we adopt sub-game perfect Nash equilibrium as our solution concept (Fudenberg and Tirole (1994)). In the next section, we first derive the equilibrium behavior in the three channel structures respectively, and then compare these results across channel structures.. 2.3. Equilibrium Analysis. In this section, we obtain the equilibrium outcomes under different channel structures. Our goal is to characterize the regions within which the manufacturers adopt different combinations of advertising strategies; we then compare how likely it is for a specific combination of advertising strategies across different channel structures. Since we focus on the strategic role of advertising, in this section we assume β = 1 to simplify the following analysis.1 In Section 2.3.3, we discuss the impact of having different values of β on the manufacturers’ advertising strategies.. 2.3.1. Advertising Equilibrium under Each Channel Structure. We first derive the advertising equilibrium under each channel structure. To this end, we must solve the game backwards by first characterizing the equilibrium pricing strategies for a given profile of advertising strategies. The nature of the pricing game and the specific timing 1. This assumption is made merely for expositional convenience; it implies that the initial sizes of the. manufacturers’ local markets and the common market are the same.. 11.

(20) of making these decisions critically depend on the channel structure, which we describe in detail below. In the integrated channel, manufacturer i’s profit can be written as: ΠIi = max pi qi , pi. i = 1, 2,. where the superscript I stands for “integrated” and the demand qi has been specified in (1). In equilibrium, each manufacturer maximizes his own profit by selecting the price. In the delegated channel, we shall first start with the retailer’s problem of determining the optimal retail price pi : πi = max {(pi − wi )qi }, i = 1, 2, pi. where wi denotes Mi ’s posted wholesale price. Accordingly, a manufacturer then determines the optimal wholesale price by solving ΠD = max wi qi , i = 1, 2, i wi. where the superscript D stands for “delegated” and qi depends on the retailer’s pricing decision through (1). Finally, in the common retailer channel, given the manufacturers’ advertising strategies and the wholesale prices, the profit of the common retailer, denoted by πR , is: πR = max {(p1 − w1 )q1 + (p2 − w2 )q2 }, p1 ,p2. and a manufacturer’s profit is: ΠC = max wi qi , i wi. i = 1, 2,. where the superscript C indicates the “common retailer channel.” With these objective functions, we can characterize the equilibrium pricing strategies for the manufacturers and the retailers. After these steps, we can then formulate conceptually the normal-form game of the manufacturers’ advertising competition in Table 1. In Table 1, Πki (s, t) denotes the manufacturer i’s profit under channel structure k ∈ {I, D, C}. The two arguments s and t correspond to the manufacturer’s own advertising strategy and its rival’s advertising strategy, where “N” means no advertising, “I” means informative advertising, 12.

(21) Table 1: Manufacturers’ Advertising Game N (No Ads). I (Informative Ads). P (Persuasive Ads). N. Πk1 (N, N), Πk2 (N, N). Πk1 (N, I), Πk2 (N, I). Πk1 (N, P ), Πk2 (N, P ). I. Πk1 (I, N), Πk2 (I, N). Πk1 (I, I), Πk2 (I, I). Πk1 (I, P ), Πk2 (I, P ). P. Πk1 (P, N), Πk2 (P, N). Πk1 (P, I), Πk2 (P, I). Πk1 (P, P ), Πk2 (P, P ). M1. M2. and “P ” means persuasive advertising. Detailed expressions of these profit functions are presented in the appendix. Table 1 allows us to derive the equilibrium advertising strategies under each channel context. For ease of exposition, we demonstrate a generic illustration for the regions of equilibrium advertising strategy profile in Figure 1, where (I, I) is the dominant-strategy equilibria in Region 1, (P, P ) in Region 3, and an asymmetric equilibrium (I, P ) or (P, I) in between these zones (labeled as Region 2). Based on Figure 1, we can derive the equilibrium advertising strategies under each channel context that are summarized in Proposition 1: Proposition 1. In all channel contexts, for any specific value of γ, there exist corresponding thresholds θak and θbk (θbk > θak , k = I, D, C) such that manufacturers engage in informative advertising whenever θ < θak but persuasive advertising whenever θ > θbk . Moreover, both thresholds θak and θbk decrease as persuasive advertising is more effective (γ decreases). As shown in Figure 1, when the products are highly substitutable, both manufacturers find it optimal to engage in persuasive advertising. On the contrary, when the product differentiation is relatively significant, informative advertising emerges as an optimal strategy for the manufacturers. In the intermediate cases, manufacturers intend to differentiate in their advertising strategies to mitigate the competition. To understand the results of Proposition 1, let us recall the strategic motives of the informative and persuasive advertising. As aforementioned in Section 2.2, informative advertising is intended to inform consumers who originally are familiar with the rival product 13.

(22) Figure 1: Advertising Equilibrium in Different Channel Contexts. (i.e., G1 or G2 ) the presence of the advertised product. Therefore, informative advertising enlarges the advertising manufacturer’s effective demand; this is referred to as the demandexpanding effect. At the same time, the invasion of the advertising manufacturer in the rival’s local market may trigger the rival’s counteraction and therefore may lead to more intense competition (referred to as the competition-enhancing effect). The demand-expanding effect works in favor of the advertising manufacturer, whereas the competition-enhancing effect may drive down his profit. On the contrary, persuasive advertising affects the preferences of consumers in the common pool (Gc ). It reduce the product substitution between m1 and m2 . This is referred to as competition-mitigating effect. At the same time, while using persuasive advertising, the manufacturer may attempt to induce a higher retail price in response to the enhanced product differentiation. This increased price in turn may make the consumers in the local market (group Gi ) unwilling to purchase from the manufacturer. We label this force as the demand-shrinking effect. The competition-mitigating effect works in favor of the advertising manufacturer, whereas the demand-shrinking effect may drive down his profit. 14.

(23) The above descriptions allow us to relate these effects to the inherent degree of product differentiation, θ, and the effectiveness of persuasive advertising, γ. Since both the demandexpanding effect and the demand-shrinking effect focus on how a consumer (either in the common pool or in the local market) responds to the price change of a manufacturer’s own product, they are not affected by the specific values of θ and γ.2 On the contrary, how strong the competition-enhancing and the competition-mitigating effects are crucially depends on these values. Specifically, when the products are close substitutes (θ is high), a manufacturer’s informative advertising is likely to induce the rival’s counteraction, thereby leading to a strong competition-enhancing effect. As γ becomes lower, persuasive advertising shifts the consumers’ preferences more effectively; thus, the competition-mitigating effect is stronger. With these taxonomies in mind, we can now articulate the strategic roles of manufacturers’ advertising. From Figure 1, when persuasive advertising is highly ineffective (a higher γ) and the product are sufficiently differentiated (a lower θ), the competition-enhancing effect is relatively insignificant and the competition-mitigating effect does not generate a high profit gain for the advertising manufacturer. Consequently, it is more profitable to engage in informative advertising and (I, I) emerges as the equilibrium outcome. However, as the products become highly substitutable (a higher θ) and persuasive advertising is highly effective (a lower γ), both the competition-enhancing effect and competition-mitigating effect will become active. This implies that informative advertising would trigger severe competition between the manufacturers; on the contrary, persuasive advertising allows the manufacturers to differentiate their markets more effectively. Consequently, persuasive advertising becomes a more favorable strategy and either (P, I) or (P, P ) occurs in equilibrium. Having discussed the common features of the equilibrium outcomes, in the remainder of this section, we compare the equilibrium outcomes across the channel structures. This allows us to articulate the strategic roles of informative and persuasive advertising under different channel structures. 2. However, these two effects are highly sensitive to β, as will be discussed in Section 2.3.3.. 15.

(24) 2.3.2. Advertising Strategies and Channel Structure. We first focus on the regions under which the manufacturers adopt informative advertising, i.e., (I, I). In order to evaluate how likely (I, I) may emerge as an equilibrium among these three channel structures, we present the regions for (I, I) under different channel structures in the same figure, Figure 2. Since (I, I) is more likely to occur when the degree of inherent product differentiation, θ, is low and the effectiveness of persuasive advertising is low (γ is high), we can conveniently use curves to identify the regions for (I, I). Specifically, in Figure 2, the left-hand sides of Curves 0, 1, and 2 are the regions for (I, I) under the common retailer channel, the integrated channel, and the delegated channel, respectively. For ease of presentation, we label these regions as RD (I, I), RI (I, I), RC (I, I) , respectively. From Figure 2, we observe that these regions are nested, i.e., RC (I, I) ⊂ RI (I, I) ⊂ RD (I, I), which leads to the following proposition.. Figure 2: Comparison of Regions for (I, I) among Three Channel Contexts. Proposition 2. The probability of observing informative advertising in equilibrium is higher in a delegated channel than in an integrated channel, which in turn is higher than in a common retailer channel. Proposition 2 shows that the equilibrium advertising strategies crucially depend on 16.

(25) the channel structure. Specifically, if we restrict to the equilibrium outcome with both manufacturers adopting informative advertising, we should expect to observe it most likely in the delegated channel, and least likely in the common retailer channel. To understand this result, let us recall the literature on the channel competition under different channel structures. Stemming from the seminal work by McGuire and Staelin (1983), it has been well known that compared to the scenario with direct (integrated) channels, selling through dedicated retailers reduces the price competition between the manufacturers.3 In this sense, dedicated retailers serve as a buffer between the manufacturers and thus are able to drive up the retail prices. On the other hand, the higher retail prices may also prevent some consumers from purchasing from these manufacturers, thereby resulting in a lower effective demand for the manufacturers. In such a scenario, the manufacturer may intend to use informative advertising to extend his potential market (by encroaching on the rival’s local market). Following the taxonomies introduced after Proposition 1, informative advertising leads to two effects: the demand-expanding and competition-enhancing effects. In both the integrated and delegated channels, the demand-expanding effect is similar. However, in the delegated channel, the competition-enhancing effect is less significant due to the retailer buffer. As the retailers are aware of the intensified competition, they tend to reduce the retail margins to counterbalance the effect of informative advertising. This in turn implies that the manufacturers are less concerned about the product competition and therefore are less inclined to counteract the rival’s invasion in his local markets. This explains why compared to the integrated channel, informative advertising is more likely to emerge as an equilibrium outcome in the delegated channel. The above argument shows that the retailer buffer promotes informative advertising. However, when both manufacturer sell through a common retailer, things are dramatically different. Recall that with a common retailer, the downstream competition vanishes. Thus, this common retailer behaves as a monopolist while facing all three groups of the consumers. 3. See also Bernheim and Whinston (1985), Bonanno and Vickers (1988), Coughlan (1985), Gupta and. Loulou (1998), Moorthy (1988), and Rey and Stiglitz (1995).. 17.

(26) Since informative advertising intensifies the product competition (by making more consumers aware of both products), a manufacturer benefits only when by doing so he attracts more consumers to purchase his own product (i.e., the demand-expanding effect). Nevertheless, it is the common retailer that determines the retail prices. As demonstrated in the appendix, even though the manufacturers intend to lower the wholesale prices upon adopting informative advertising, the common retailer will accordingly set a high retail margin that offsets/ mitigates the demand-expanding effect. This is because the common retailer does not aim at increasing the market share of a particular manufacturer; rather, she attempts to choose the retail prices that maximally extract the revenue from the consumers. This counteraction (from the common retailer) makes informative advertising unfavorable from the manufacturers’ perspective. Notably, although both the dedicated retailers and the common retailer serve as buffers that mitigate the head-to-head competition between the manufacturers, these different indirect channels lead to very different incentives of adopting informative advertising as discussed above. The nature of the competition in the downstream consequently affects the upstream manufacturers’ strategic concerns of adopting their advertising strategies. It is also worth mentioning that the extant literature on advertising strategies focuses exclusively on the integrated (direct) channel. Under this channel structure, it is not surprising that persuasive advertising is more favorable from the manufacturers’ viewpoints because it enhances product differentiation. Researchers consequently predict that the manufacturers provide too little informative advertising (Stegeman (1991)), whereas persuasive advertising is carried out at an excessive level (Dixit and Norman (1978), Nichols (1985), and Stigler and Becker (1977). Our results compensate this research stream by linking the channel structure to the manufacturers’ incentive of offering informative/ persuasive advertising, and highlight the strategic interactions along the distribution channel. Proposition 2 demonstrates the tight connection between the channel structure and the manufacturers’ incentives. Conceivably, it is possible that under different channel structures the manufacturers may intend to use different advertising strategies. To address this issue, we combine the three sub-figures in Figure 1 into Figure 3, where the six curves correspond to. 18.

(27) Figure 3: Difference in Advertising Strategies across Three Channel Contexts. the boundaries beyond which (I, I) or (P, P ) emerges as the equilibrium of the manufacturers’ advertising game under each channel structure, respectively. Figure 3 shows that (P, P ) is most likely to be sustained as an equilibrium in the common retailer channel, followed by the integrated channel and the delegated channel, in descending order. This is because the common retailer behaves as a monopolist; consequently the more differentiated the manufacturers’ products are, the more profit the common retailer can extract from the consumers. As the common retailer earns a higher profit from the consumers, the manufacturers can accordingly set a higher wholesale price to appropriate more revenue from the retailer.4 This suggests that the manufacturers have a strong incentive to promote product differentiation (by adopting persuasive advertising) while selling through a common retailer. On the other hand, (I, I) is the most likely to be an equilibrium in the delegated channel, followed by the integrated channel and the common retailer channel. The rationale for this has been discussed in Proposition 2. A more interesting observation is that the boundary curves of (I, I) for the delegated and 4. A relatively subtle point here is that the retailer does not increase the retail margin too much despite the. enhanced product differentiation. As we verify in the appendix, the monopoly common retailer is concerned about the effective demand and consequently she chooses a reasonable retail margin and gives away a large proportion of the increased margin to the manufacturers.. 19.

(28) integrated channels lie in the right-hand side of the curve of (P, P ) for the common retailer channel. This implies that there exists a region A1 for (θ, γ) in which the manufacturers adopt persuasive advertising in the common retailer channel, but adopt informative advertising in either the integrated or the delegated channel. Likewise, we find that the boundary curves of (P, P ) for the integrated and common retailer channels lie in the left-hand side of the curve of (I, I) for the delegated channel. Thus, there exists a region A2 for (θ, γ) in which the manufacturers adopt informative advertising in the delegated channel, but adopt persuasive advertising in either the integrated or the common retailer channel. Collectively, we obtain our main result: Proposition 3. The manufacturers’ advertising strategies critically depend on the channel structure. Specifically, 1. (P, P ) is the most likely to be sustained as an equilibrium in the common retailer channel, followed by the integrated channel and the delegated channel, in descending order. On the other hand, (I, I) is the most likely to be an equilibrium in the delegated channel, followed by the integrated channel and the common retailer channel. 2. There are scenarios in which the manufacturers adopt different advertising strategies under different channel structures. Our results offer a managerial direction for the management of advertising role to fit in with channel structure strategy in view of competition. Despite the pro-competitive nature of informative advertising and anti-competitive nature of persuasive advertising, the manufacturers do not necessarily benefit from adopting persuasive advertising. There are three driving forces in tension that determine the optimal choice of advertising strategies: the channel structure, the inherent product differentiation, and the effectiveness of persuasive advertising. As aforementioned, the manufacturers prefer different intensities of competition (between products) under different channel structures to balance the trade-off between the retailer buffer and the double marginalization. Furthermore, persuasive advertising is more likely to be adopted if either it is more effective or the product are insufficiently differentiated (from the manufacturers’ perspective). 20.

(29) 2.3.3. Discussions. We now briefly discuss the impact of the size of the consumers in the common pool (Gc ). In our model, this can be conveniently incorporated by varying the value of β: as β becomes larger, the size of Gc becomes relatively larger (compared to those local consumers (G1 and G2 ). The size change of the consumer markets therefore affects the demand-expanding and demand-shrinking effects. When the size of Gc becomes relatively larger (β becomes larger), the manufacturers are more concerned about the demand from the common pool than that from the local consumers (Gi ). This implies that the demand-expanding effect is less significant while informative advertising is adopted. Nevertheless, the demand-shrinking effect that arises from persuasive advertising is unaffected. Collectively, the manufacturers are more inclined to adopt persuasive advertising while facing a larger common pool, thereby enlarging the region in which (P, P ) emerges as the equilibrium outcomes (i.e., shifting the boundaries of (P, P ) to the left). This phenomenon is not prone to the specific channel structure. Notably, the comparison of the equilibrium outcomes among channel structures remains to be valid, since the increase of β only strengthens the manufacturers’ incentive to adopt persuasive advertising but does not affect their temptation to adjust the appropriate intensity of competition in response to the channel structure.. 2.4. Concluding Remarks. In this chapter, we provide a unified framework towards a thorough understanding of the interplay between the advertising strategies and the channel structure. Specifically, we show that when manufacturers delegate the sales responsibility to dedicated retailers, informative advertising may yield a higher profit for the manufacturers due to its pro-competitive nature. On the contrary, persuasive advertising should be used more extensively when either the manufacturers sell directly to the end consumers or sell through a common retailer. This is because different advertising strategies allow the manufacturers to adjust the appropriate competition intensity. Consequently, the manufacturers may strategically adopt different advertising strategies in different channel structures, taking into account the competition/ 21.

(30) monopoly in the downstream market. We also identify operating regions under which one form of advertising strategy is more favorable than the other, thereby providing a handy guideline for practitioners to design their advertising strategically. Several extensions are in order. In our model, the manufacturers are endowed with the full bargaining power and consequently are able to determine the wholesale prices in favor of themselves. Nevertheless, there are situations in which it is the retailer that possess a higher bargaining power. In such a scenario, the relative bargaining power may affect how the manufacturers value the advertising strategies and consequently lead to different conclusions from this chapter. Second, one could also consider more complicated channel structures. For example, when there are multiple manufacturers and multiple retailers, the network structure becomes crucial and complex. For example, a manufacturer could sell through only a subset of retailers, and a retailer carries the products from a subset of manufacturers. Strategic interactions in a general channel network deserve further investigations. Finally, this chapter focuses exclusively on the manufacturers’ incentive of adopting advertising strategies, whereas in reality the retailers may also be able to advertise by themselves (e.g., to inform consumers the retail store location, price promotion, etc.). This informative advertising may be supported or discouraged by the manufacturers depending on the channel structure, and is clearly a research priority.. Appendix Derivations of the profits in the pricing games In the following, we derive the profits in the pricing games under each channel structure (i.e., those profit terms specified in Table 1). Since different advertising strategies only result in different parameters in the effective demands of the manufacturers’ products, these pricing games are similar for a given channel structure. Thus, for ease of illustration, we only present the pricing game for one combination of advertising strategies under each channel structure. Specifically, we present the case of (I, P ) for the integrated channel, (I, I) for. 22.

(31) the delegated channel, and (P, P ) for the common retailer channel. The other cases can be derived similarly. 1) (I, P ) under the integrated channel: Suppose that M1 adopts the informative advertising and M2 adopts the persuasive advertising. The demands for M1 and M2 are respectively q1 =. 3 3 3 3 5 1 − (5 + 3θ)p1 + γθp2 , and q2 = − (1 + γθ)p2 + θp1 . 2 2 2 2 2 2. Given the effective demand functions, we can solve the profit-maximization problems for both manufacturers as follows: 5 1 3 3 3 3 max Π1 = p1 [ − (5 + 3θ)p1 + γθp2 ], and max Π2 = p2 [ − (1 + γθ)p2 + θp1 ]. p1 p 2 2 2 2 2 2 2 Applying the first-order conditions to these two profit functions simultaneously, we obtain that pI1 (I, P ) =. 10 + 13γθ 10 + 11θ , and pI2 (I, P ) = . 2 4(5 + 3θ)(1 + γθ) − 3γθ 4(5 + 3θ)(1 + γθ) − 3γθ2. Thus, the corresponding demand functions and the maximum profits for the manufacturers can be expressed as follows: (5 + 3θ)(10 + 13γθ) 3(10 + 11θ)(1 + γθ) , and q2I (I, P ) = , 2 2[4(5 + 3θ)(1 + γθ) − 3γθ ] 2[4(5 + 3θ)(1 + γθ) − 3γθ2 ] (5 + 3θ)(10 + 13γθ)2 3(1 + γθ)(10 + 11θ)2 I , and Π (I, P ) = . ΠI1 (I, P ) = 2 2[4(5 + 3θ)(1 + γθ) − 3γθ2 ]2 2[4(5 + 3θ)(1 + γθ) − 3γθ2 ]2 q1I (I, P ) =. 2) (I, I) under the delegated channel: When both manufacturers adopt informative advertising, the effective demands for M1 and M2 are q1 = 2(1 − p1 ) + 2θ(p2 − p1 ), and q2 = 2(1 − p2 ) + 2θ(p1 − p2 ). Since in the delegated channel, the manufacturers determine the wholesale prices first and then the retailers set retail margins (retail prices) accordingly, by backward induction, we shall first focus on the retailers’ pricing game given the manufacturers’ wholesale prices, and then return to the manufacturers’ pricing game. 23.

(32) Given the wholesale prices, the retailers solve the following profit-maximization problems simultaneously: max π1 = (p1 − w1 )[2(1 − p1 ) + 2θ(p2 − p1 )], and max π2 = (p2 − w2 )[2(1 − p2 ) + 2θ(p1 − p2 )]. p1. p2. First-order conditions imply that p1 =. 2(1 + θ)2 w1 + θ (1 + θ) w2 1 2(1 + θ)2 w2 + θ (1 + θ) w1 1 + , and p2 = + . 2+θ (2 + θ) (2 + 3θ) 2+θ (2 + θ) (2 + 3θ). Having derived the retailers’ optimal retail prices, we now characterize the manufacturers’ wholesale prices. Given p1 and p2 , the demands for the manufacturers are respectively q1 = q2. 2 (1 + θ) 2 (1 + θ) (2 + 4θ + θ2 ) 2θ (1 + θ)2 − w1 + w2 , 2+θ (2 + θ) (2 + 3θ) (2 + θ) (2 + 3θ). 2 (1 + θ) 2 (1 + θ) (2 + 4θ + θ2 ) 2θ (1 + θ)2 = − w2 + w1 . 2+θ (2 + θ) (2 + 3θ) (2 + θ) (2 + 3θ). The manufacturers’ problems are therefore the following: # " 2 (1 + θ) 2 (1 + θ) (2 + 4θ + θ2 ) 2θ (1 + θ)2 − w1 + w2 , and max Π1 = w1 w1 2+θ (2 + θ) (2 + 3θ) (2 + θ) (2 + 3θ) " # 2 (1 + θ) 2 (1 + θ) (2 + 4θ + θ2 ) 2θ (1 + θ)2 max Π2 = w2 − w2 + w1 . w2 2+θ (2 + θ) (2 + 3θ) (2 + θ) (2 + 3θ) We can apply the first-order conditions simultaneously to solve the wholesale price game, and obtain the optimal wholesale prices as follows: w1D (I, I) = w2D (I, I) =. 2 + 3θ . 4 + 7θ + θ2. The corresponding equilibrium demands and profits for the manufacturers are respectively 2 (1 + θ) (2 + 4θ + θ2 ) = = , (2 + θ) (4 + 7θ + θ2 ) 2 (1 + θ) (2 + 3θ) (2 + 4θ + θ2 ) D ΠD . 1 (I, I) = Π2 (I, I) = (2 + θ) (4 + 7θ + θ2 )2 q1D (I, I). q2D (I, I). 3) (P, P ) under the common retailer channel:. 24.

(33) Under the common retailer channel, we focus on the scenario in which both M1 and M2 adopt persuasive advertising. The effective demands for M1 and M2 are respectively q1 = 2 − (2 + γθ) p1 + γθp2 , and q2 = 2 − (2 + γθ) p2 + γθp1 . By backward induction, we first solve the common retailer’s problem of finding the optimal retail prices. Given the manufacturers’ wholesale prices w1 and w2 , the common retailer’s goal is to find the retail prices p1 , p2 to solve the following problem: max πR = (p1 − w1 )[2 − (2 + γθ) p1 + γθp2 ] + (p2 − w2 ) [2 − (2 + γθ) p2 + γθp1 ] . p1 ,p2. Applying the first-order conditions, we obtain that p1 =. 1 + w2 1 + w1 , and p2 = , 2 2. and the corresponding demands for the manufacturers are respectively γθ γθ γθ γθ q1 = 1 − 1 + w1 + w2 , and q2 = 1 − 1 + w2 + w1 . 2 2 2 2 Now we return to the manufacturers’ problem of finding the optimal wholesale prices: γθ γθ γθ γθ max Π1 = w1 1 − 1 + w1 + w2 , and max Π2 = w2 1 − 1 + w2 + w1 . w1 w2 2 2 2 2 Solving them simultaneously, we obtain the equilibrium wholesale prices as follows: w1C (P, P ) = w2C (P, P ) =. 2 , 4 + γθ. and the corresponding equilibrium demands and profits for the manufacturers are respectively 2 + γθ , 4 + γθ 2 (2 + γθ) C ΠC . 1 (P, P ) = Π2 (P, P ) = (4 + γθ)2 q1C (P, P ) = q2C (P, P ) =. 25.

(34) Summary of the results in the advertising games We now summarize our results in the advertising games under the three channel structures and illustrate them via graphic representations. 1) Integrated channel: Let us first consider the integrated channel. The profits under different combinations of advertising strategies are summarized below: 4(2 + θ) , (4 + θ)2 3(1 + θ)(10 + 11θ)2 I Π2 (I, N) = , 2(20 + 32θ + 9θ2 )2 (5 + 3θ)(10 + 13θ)2 ΠI1 (I, N) = , 2(20 + 32θ + 9θ2 )2 4(2 + θ)(4 + 3γθ)2 , ΠI2 (P, N) = [4(2 + θ)(2 + γθ) − γθ2 ]2 4(2 + γθ)(4 + 3θ)2 ΠI1 (P, N) = , [4(2 + θ)(2 + γθ) − γθ2 ]2 2(1 + θ) ΠI2 (I, I) = , (2 + θ)2 (5 + 3θ)(10 + 13γθ)2 ΠI2 (P, I) = , 2[4(5 + 3θ)(1 + γθ) − 3γθ2 )2 3(1 + γθ)(10 + 11θ)2 I , Π1 (P, I) = 2[4(5 + 3θ)(1 + γθ) − 3γθ2 )2 4(2 + γθ) ΠI2 (P, P ) = . (4 + γθ)2. ΠI1 (N, N) = ΠI2 (N, N) = ΠI1 (N, I) = ΠI2 (N, I) = ΠI1 (N, P ) = ΠI2 (N, P ) = ΠI1 (I, I) = ΠI1 (I, P ) = ΠI2 (I, P ) = ΠI1 (P, P ) =. Note that in the manufacturers’ profits, when both manufacturers do not adopt any advertising strategy, both manufacturers receive a higher profit as the product differentiation is more significant (θ is higher). However, this no longer holds if one of the manufacturers adopts the informative/ persuasive advertising. The three plots a, b, c in Figure 2.4 show the profits of Mj between different advertising responses under different advertising strategies by Mi . The contour is the set of points for which manufacturer Mj is indifferent between adopting informative advertising and adopting persuasive advertising. From Figure 2.4, we observe that Mj ’s best response is informative 26.

(35) Figure 4: Advertising Equilibrium Analysis in the Integrated Channel. advertising if (θ, γ) falls in the left-hand side of the contour, whereas the right-hand side corresponds to the region in which persuasive advertising becomes more favorable. We combine the three plots a, b, and c in d in Figure 2.4 to show that the manufacturers’ dominant strategy is informative advertising in Region 1; consequently, the equilibrium is (I, I). On the other hand, the manufacturers’ dominant strategy is persuasive advertising in Region 3, thereby leading to the equilibrium (P, P ). 2) Delegated channel: In the delegated channel, the manufacturers’ profits under different combinations of advertising strategies are as follows: D ΠD 1 (N, N) = Π2 (N, N) =. 4 (2 + θ) (4 + 3θ) (8 + 8θ + θ2 ) , (4 + θ) (16+14θ + θ2 )2 2. ΠD 1 (N, I) =. 3 (1 + θ) (10 + 16θ + 3θ2 ) (200 + 590θ + 507θ2 + 105θ3 ) , 2 (20 + 32θ + 9θ2 ) (400 + 1280θ + 1249θ2 + 360θ3 + 27θ4 )2 2. (5 + 3θ) (10 + 16θ + 3θ2 ) (2 + 3θ)2 (100 + 155θ + 37θ2 ) , 2 (20 + 32θ + 9θ2 ) (400 + 1280θ + 1249θ2 + 360θ3 + 27θ4 )2 (2 + θ) (8 + 4θ + 4γθ + γθ2 )kd1 2 ΠD (N, P ) = , 1 (4 (2 + θ) (2 + γθ) − γθ2 )kd2 2 ΠD 2 (N, I) =. 27.

(36) ΠD 2 (N, P ). =. ΠD 1 (I, N) = ΠD 1 (I, I) = ΠD 1 (I, P ) = ΠD 2 (I, P ) = ΠD 1 (P, N) =. where. (2 + γθ) (8 + 4θ + 4γθ + γθ2 )kd3 2 , (4 (2 + θ) (2 + γθ) − γθ2 )kd4 2 D D ΠD 2 (N, I), Π2 (I, N) = Π1 (N, I) 2 (1 + θ) (2 + 3θ) (2 + 4θ + θ2 ) ΠD (I, I) = , 2 (2 + θ) (4+7θ + θ2 )2 (5 + 3θ) (10 + 6θ + 10γθ + 3γθ2 ) kd5 2 , 2 (4 (1 + γθ) (5 + 3θ) − 3γθ2 )kd6 2 3 (1 + γθ) (10 + 6θ + 10γθ + 3γθ2 ) kd7 2 , 2 (4 (1 + γθ) (5 + 3θ) − 3γθ2 )kd8 2 D D ΠD 2 (N, P ), Π2 (P, N) = Π1 (N, P ),. D D D ΠD 1 (P, I) = Π2 (I, P ), Π2 (P, I) = Π1 (I, P ), 4 (2 + γθ) (4 + 3γθ) (8 + 8γθ + γ 2 θ2 ) D , ΠD (P, P ) = Π (P, P ) = 2 1 2 (4 + γθ) 16+14γθ + γ 2 θ2. kd1 = 4 (4 + 3γθ) 8 + 4θ + 4γθ + γθ2 + 2γθ (2 + γθ) (4 + 3θ) , 2 kd2 = 4 8 + 4θ + 4γθ + γθ2 − γθ2 (2 + θ) (2 + γθ) , kd3 = 4 (4 + 3θ) 8 + 4θ + 4γθ + γθ2 + 2θ (2 + θ) (4 + 3γθ) , 2 kd4 = 4 8 + 4θ + 4γθ + γθ2 − γθ2 (2 + θ) (2 + γθ) , kd5 = 2 (10 + 13γθ) 10 + 6θ + 10γθ + 3γθ2 + 3γθ (10 + 11θ) (1 + γθ) , 2 kd6 = 4 10 + 6θ + 10γθ + 3γθ2 − 3γθ2 (1 + γθ) (5 + 3θ) , kd7 = 2 (10 + 11θ) 10 + 6θ + 10γθ + 3γθ2 + θ (5 + 3θ) (10 + 13γθ) , 2 kd8 = 4 10 + 6θ + 10γθ + 3γθ2 − 3γθ2 (1 + γθ) (5 + 3θ) . The graphic illustration is given in Figure 5, which follows the same spirit as in Figure 4. We again observe that in Region 1, the manufacturers’ dominant strategy is informative advertising, and the equilibrium is (I, I); on the contrary, the dominant strategy is persuasive advertising, and the equilibrium is (P, P ) in Region 3. 3) Common retailer channel: The manufacturers’ profits while delegating to a common retailer under different com-. 28.

(37) Figure 5: Advertising Equilibrium Analysis in the Delegated Channel. binations of advertising strategies are as follows: 2(2 + θ) 3 (1 + θ) (10 + 11θ)2 C = = , Π1 (N, I) = , (4 + θ)2 4(20 + 32θ + 9θ2 )2 (5 + 3θ) (10 + 13θ)2 C , Π2 (N, I) = 4(20 + 32θ + 9θ2 )2 16(2 + θ)kc1 2 , ΠC (N, P ) = 1 (2 + θ + γθ) 4 (2 + θ) (2 + γθ) − θ2 (1 + γ)2 kc22. ΠC 1 (N, N). ΠC 2 (N, P ) =. ΠC 2 (N, N). 16(2 + γθ)kc3 2 , (2 + θ + γθ) 4 (2 + θ) (2 + γθ) − θ2 (1 + γ)2 kc42. C C C ΠC 1 (I, N) = Π2 (N, I), Π2 (I, N) = Π1 (N, I) (1 + θ) C ΠC , 1 (I, I) = Π2 (I, I) = (2 + θ)2 (5 + 3θ) [(4+4γθ)((5 + 3θ) (10 − 3θ + 7γθ) + 3θ (10γ + γθ − 5θ)) + kc5 ]2 ΠC (I, P ) = , 1 (5 + 3θ + 5γθ) 4 (5 + 3θ) (1 + γθ) − 3 (1 + γ)2 θ2 kc6 2 3 (1 + γθ) [4 (5 + 3θ) ((1 + γθ) (10 + θ − 5γθ) + θ (10 + 7γθ − 3γ 2 θ)) + kc7 ]2 ΠC , 2 (I, P ) = (5 + 3θ + 5γθ) 4 (5 + 3θ) (1 + γθ) − 3 (1 + γ)2 θ2 kc8 2. C C C C C C C ΠC 1 (P, N) = Π2 (N, P ), Π2 (P, N) = Π1 (N, P ), Π1 (P, I) = Π2 (I, P ), Π2 (P, I) = Π1 (I, P ), 2 (2 + γθ) C ΠC , 1 (P, P ) = Π2 (P, P ) = (4 + γθ)2 29.