Uniform and Targeted Advertising with Shoppers and. Asymmetric Loyal Market Shares

Transcription

1 Uniform and Targeted dvertising with Shoppers and symmetric Loyal Market Shares Michael rnold, Chenguang Li and Lan Zhang October 9, 2012 Preliminary and Incomplete Keywords: informative advertising, targeted advertising, uniform advertising, asymmetric markets, shoppers, loyal customers bstract This paper explores the strategic tradeoff between advertising and pricing strategies when firms have asymmetric loyal market segments and also can compete for shoppers who purchase at the lowest advertised price. Three advertising structures consistent with real world settings are considered. In the first setting firms are limited to advertising campaigns that reach the entire market and present all consumers with a uniform price. The analysis is then extended to allow firms to target ads to ecific market segments (either with both firms targeting ads or with only one firm having the ability to target). In all cases our analysis demonstrates how asymmetric loyal market segments impact the equilibrium tradeoff between advertising intensity and price competition in interesting ways not revealed by the existing literature which largely assumes firms compete in a symmetric environment. Department of Economics, lfred Lerner College of Business and Economics, University of Delaware, Newark, DE 19716, marnold@udel.edu JP Morgan Chase, chenguang.x.li@chase.com Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu, China, zhanglan@swufe.edu.cn 1

2 1 Introduction critical question facing firms when making advertising and pricing decisions in order to capture shoppers is how the advertising and pricing strategy adopted by the firm impacts overall price competition and equilibrium profits. In markets with loyal customers and shoppers, advertising a low price to capture the shopping segment of the market may result in Bertrand price competition and zero profits for all firms in the market. More strategic alternatives require firms to seek a balance between advertising intensity and price competitiveness. n increase in advertising intensity (holding one s pricing strategy fixed) might induce increasingly competitive pricing from other players in the market. Similarly, a change in one s pricing strategy (to a less aggressive pricing distribution, for example), might impact the competition s equilibrium advertising intensity. This paper explores the strategic trade-off between advertising and pricing strategies when firms have asymmetric loyal market segments and also can compete for shoppers who purchase at the lowest advertised price. Three advertising structures consistent with real world settings are considered. In the first setting firms are limited to uniform advertising campaigns that reach the entire market and present all consumers with the same price. We then consider options to target ads to ecific segments (either with both firms targeting ads or with only one firm having the ability to target). In all cases our analysis demonstrates how the presence of asymmetric loyal segments has interesting implications for the equilibrium trade-off between advertising intensity and price competition. The main contribution of our analysis stems from incorporating asymmetric firms in an environment requiring informative price advertising. Most of the literature on informative advertising and pricing is restricted to the case of symmetric loyal market shares. The literature on promotional pricing strategies includes analyses of asymmetric firms, but typically does not consider the role of informative advertising to communicate prices to consumers. Rather, price competition occurs with some consumers ( shoppers ) knowing all prices and others ( uninformed or loyal consumers) only observing prices charged by a subset of the firms in the market. Our analysis enhances understanding of informative advertising and price competition by simultaneously considering asymmetries consistent with real-world market structures with the mechanism by which price information is communicated to consumers. For example, our analysis demonstrates that if consumers learn about pricing through uniform price advertisements distributed to all consumers, 2

3 then the firm with the larger loyal market will price less competitively but advertise more aggressively than the firm with the smaller loyal share. However, if a firm can target advertising to its own loyal segment and the shopping segment of the market, then the firm with the large loyal share advertises less intensely and prices more aggressively than the firm with the smaller share. There is a large literature exploring price competition without advertising in both symmetric and asymmetric settings. For example, in Varian s (1980) model of sales symmetric firms compete in price in a market with both informed and uninformed consumers. The uninformed consumers are allocated equally across firms, and the informed consumers purchase from the firm with the lowest price. Varian demonstrates that firms adopt a symmetric mixed pricing strategy and earn positive expected profits in equilibrium. Baye, Kovenock and de Vries (1992) extend Varian s model to the case of n > 2 firms and show that while there are multiple, asymmetric Nash equilibria, there is a unique symmetric subgame perfect equilibrium. Narasimhan (1988) was among the first to consider price competition between asymmetric firms. He modeled a duopoly market in which the firms have asymmetric loyal market segments and also compete for shoppers who purchase at the lowest price. His analysis finds that the firm with the larger loyal share prices less competitively in equilibrium than the firm with the small loyal share. In particular, the firm with the large loyal share is less likely to offer a discount off the monopoly price, but offers the same average discount when it does discount from the monopoly price. Our analysis demonstrates that when consumers only learn of a firm s price through uniform advertising, the firm with the larger share prices less aggressively and may offer a smaller average discount off the monopoly price, when it does discount, than the firm with the smaller share. This occurs because the firm with the smaller share may adopt a mixed advertising strategy which makes it less of a competitive threat than in Narasimhan s model in which firms do not make advertising decisions. Others have built on Narasimhan s work in a price competition framework with no advertising. Deneckre, Kovenock and Lee (1992) consider a two period price leadership duopoly game and show that the firm with the smaller loyal share prefers to be the follower. Kocas and Kiyak (2008) consider n > 2 firms and find that only the firms with the two smallest loyal markets compete for shoppers by offering discounts off the monopoly price. ll other firms charge the monopoly price and sell only to their loyal customers. Jing and Wen (2008) show how Narasimhan s results change if loyalty to the firm with the larger share is suffi ciently limited (so that consumers loyal to the larger firm switch to the 3

4 competitor if the price differential exceeds a threshold). None of these extensions consider the role of informative advertising to communicate price information. nother strand of literature focuses on informative price advertising in a symmetric setting. This literature contains two branches. One considers the presence of a gatekeeper through which prices can be advertised to the shopping segment of consumers who only purchase if the product is advertised, while loyal customers always purchase the product from their preferred firm regardless of whether an advertisement is posted through the gatekeeper. Baye and Morgan (2001) consider a clearinghouse model with n identical firms which each serve a local market and can compete for shoppers by advertising through a gatekeeper. Equilibrium is characterized by firms adopting symmetric advertising and mixed pricing strategies and by persistent price diersion. In a similar setting with symmetric firms Renhoff and Serfes (2009) show that dilay advertising (which functions similarly to the gatekeeper in the Baye and Morgan model) can correond to increased price competition consistent with observations from scanner panel data. rnold, Li, Saliba and Zhang (2011) analyze an asymmetric, duopoly version of the gatekeeper model and show that the firm with the smaller loyal market share advertises more intensely but prices less competitively than the firm with the large loyal market. second branch of this literature considers informative advertising in which customers are only aware of the product, and the firms selling the product, if a price is advertised. Three cases of informative price advertising are of interest. Under uniform advertising, firms are restricted to a choice between advertising a single price to all consumers in the market or not advertising at all (and therefore, not participating in the market). Targeted advertising, on the other hand, enables firms to target advertisements either to the firm s own loyal market segment or the loyal segment and the shoppers, without having to expend resources advertising to the competing firm s loyal customers. Targeted advertising may or may not allow for price discrimination across the two segments. Iyer, Soberman and Villas-Boas (2005) analyze advertising strategies in a duopoly model with symmetric loyal market shares when competing firms can target advertising to different groups of consumers. In equilibrium firms adopt symmetric mixed advertising and pricing strategies and advertise more intensely to loyal customers than to shoppers. In contrast, we show that with asymmetric loyal market shares, at least one of the two firms always advertises to the shoppers with probability one. The present paper combines the price competition and informative advertising streams of lit- 4

5 erature by developing a duopoly model of informative advertising with asymmetric loyal customer shares in which customers only consider purchasing the product if a price is advertised. 1 Loyal consumers only purchase if their preferred firm advertises and shoppers buy from the firm offering the lowest price. Each firm makes two strategic decisions, namely whether or not to advertise and, conditional on advertising, the price to post. In contrast to earlier literature, we find that with asymmetric loyal segments, one of the firms always adopts a pure advertising strategy. Under uniform advertising, the firm with the larger loyal customer base advertises with probability one, both firms adopt mixed pricing strategies, and the firm with the smaller loyal share prices more aggressively. With positive advertising costs, the firm with more loyal consumers advertises with probability one to ensure sales to its large loyal base but prices less competitively (on average) to avoid selling at a discount to its loyal customers. When both firms can target advertising and sets a uniform price, each firm will, at a minimum, advertise to its own loyal segment. The decision to also compete for the shopping segment requires more competitive pricing (on average) but also increases the number of potential customers. The firm with the larger loyal share manages this trade-off with a mixed advertising and pricing strategy while the firm with the smaller loyal share advertises to shoppers with probability one. In balancing the equilibrium trade-off between advertising and price competition, the firm with the smaller loyal share advertises more intensely, but adopts a less competitive pricing strategy in order to avoid selling to its loyal customers at a low price. The firm with the larger loyal share advertises to shoppers less intensely so as not to incent deeper discounts by the competing firm and to avoid selling at a lower price to its larger share of loyal customers. However, when it does advertise, it prices aggressively to increase the chance that it wins the shoppers in order to justify selling to its loyal customers at a lower price. The remainder of the paper is organized as follows. The model is presented in section 2. Sections 3 and 4 analyze advertising and pricing behavior under uniform advertising and targeted advertising, reectively. Finally, we conclude in section 5. 1 Two interesting papers by Chiovenau (2009) and Eaton MacDonald and Meriluoto (2010) show how asymmetric loyal shares arise endogenously in a model of persuasive (or existence) advertising in which firms advertise to attract loyal market shares. Both papers consider a subgame perfect equilibrium of a game in which the second stage entails price competition with no advertising after asymmetric shares are established in the first stage. 5

6 2 The Model Consider a market with two firms, i = 1, 2 which produce a product at a constant marginal cost c i which is assumed to be zero without loss of generality. The market is comprised of a unit mass of consumers who are only aware of product availability at a given firm if that firm advertises its product. In the analysis below the firms are initially restricted to a uniform advertising strategy under which a decision to advertise results in a single price being advertised to all consumers. We then extend the analysis to allow for targeted advertising which enables a firm to limit its advertising to a ecific segment of consumers. The consumers, all of whom have the same reservation price r for one unit of the product, are segmented into three groups. fraction h 1 > 0 of the consumers are loyal to firm 1 in the sense that they will never purchase from firm 2. Similarly, a fraction h 2 < h 1 are loyal to firm 2. The remaining fraction s 1 h 1 h 2 > 0 are shoppers who purchase from the firm advertising the lowest price (and do not purchase if neither firm advertises). We refer to consumers in the segment h 1 as type 1 consumers, to those in the segment h 2 as type 2 consumers, and to those in the segment s as shoppers. The existence of three distinct segments could arise for several reasons. For example, location differences and travel costs could lead to three segments those who work and live near firm 1 and will not travel to firm 2, those work and live near firm 2 and will not travel to firm 1, and those who live near one firm and work near the other who purchase from the firm offering the lowest price. The segmentation is also consistent with a product differentiation scenario in which some consumers have a strong preference for unique attributes of firm 1 s product, others have a strong preference for the unique attributes of firm 2 s product, and still others are indifferent between the two products. We assume buyers are willing to pay a maximum of r for one unit of the product. 2 The cost to advertise to the entire market is for both firms. When advertising can be targeted to particular segments in the market, we assume that the cost to advertise to each segment is linearly related to its size. Therefore, if firm 1 is able to target advertising, the cost to advertise to its loyal consumers is h 1 and to shoppers is s. 2 We also have analyzed the case in which some proportion α of each consumer type purchase the product even without advertising. The results are not qualitatively different, so our model is consistent with promotional strategies for both new products (search goods) and experience goods. 6

7 2.1 Uniform Price dvertising without Targeting Suppose that neither firm has the ability to advertise to ecific segments of the market. Under uniform advertising, a firm can choose either to reach the entire market at a cost, or to not advertise at all. Denote the minimum price a firm will ever consider advertising by p i, i = 1, 2. This price equates the profit p i (h i + s) the firm can achieve by advertising a price suffi ciently low to sell to its loyal customers and the shoppers with the profit h i r the firm can achieve by advertising a price of r and selling only to its loyal customers, so p i = h i r/ (h i + s) for i = 1, 2. (1) } These minimum prices play an important role in the analysis. Let p max {p 1, p 2, and note that h 1 > h 2 implies p = p 1 = h 1 r/ (h 1 + s). In any equilibrium p is the minimum price that either firm would advertise. 3 Suppose that the advertising cost is suffi ciently low that both firms advertise with probability one in equilibrium (the condition for this is ecified in Proposition 1 below). In this case, the equilibrium pricing decisions for each firm are equivalent to those in the model considered by Narasimhan (1988). Thus, if both firms advertise with probability 1, then Narasimhan s results imply that each firm adopts mixed pricing strategies in equilibrium. 4 Furthermore, each firm must attain at least the profit h i r that it can achieve by advertising and selling to its loyal segment at the monopoly price r. However, firm 2 can exceed this profit by advertising p 1 (with probability 1). By advertising p 1 firm 2 captures the shoppers and earns a profit of (rh 1 / (h 1 + s)) (h 2 + s) which exceeds rh 2 because h 1 > h 2. Let F i (p) denote the equilibrium mixed pricing strategy cumulative distribution function for firm i. Noting that the probability that firm i captures the shoppers when advertising a price p is 3 Well known arguments imply it is never optimal for firm 2 to charge p 2 [p 2, p 1 ). 4 The intuition for this result is straightforward. pure pricing strategy with an advertised price less than r is only optimal if the firm captures the shopping segment of the market. However, if one firm captures the shoppers with a price less than r, then the other firm should either undercut that firm or forego the shoppers and charge the reservation price r. In either case, the price less than r is not an equilibrium for the first firm. Furthermore, neither the monopoly solution (r, r) nor the competitive outcome (0, 0) constitute an equilibrium because in the former case one firm can undercut its the other to ensure it captures the shoppers, and in the later case, either firm can make strictly positive profits by advertising p i = r and selling only to its loyal market segment. 7

8 (1 F j (p)), the following conditions characterize the equilibrium pricing strategies: p (h 1 + (1 F 2 (p)) s) = h 1 r (2) and p (h 2 + (1 F 1 (p)) s) = h 1 r h 2 + s h 1 + s (3) where equation (2) equates firm 1 s expected profit from advertising a price p < r with the profit from advertising r and selling only to its own loyal segment, and equation (3) equates firm 2 s expected profit from advertising p < r with the profit from advertising the minimum price p 1 and capturing the shoppers. 5 These conditions generate F 1 (p) = 1 + h 2 s 0, p < h 1r, rh 1 () (), h 1 r p < r, 1, p r. (4) and, F 2 (p) = 0, p < h 1r, 1 h 1(r p), h 1 r p r, 1, p r. (5) The results above assume that both firms advertise with probability 1. However, if > (h 1 + s) r, then neither firm will advertise because the maximum profit from advertising is strictly negative. If (h 1 + s) r > > (h 2 + s) r, then firm 2 will never advertise and firm 1 will advertise a price of r with probability 1. Similarly, if is suffi ciently low, then both firms will advertise with probability 1. Using the equilibrium strategies above, firm profits are π 1 = h 1 r and π 2 = (h 1 r/ (h 1 + s)) (h 2 + s). Because h 1 > h 2, if < (h 1 r/ (h 1 + s)) (h 2 + s), then both firms accrue strictly positive profit by advertising. If is in the interval [(h 1 r/ (h 1 + s)) (h 2 + s), (h 2 + s) r], then firm 2 s expected profit from advertising with probability 1 is negative given firm 1 also advertises with probability 1. However, if firm 2 does not advertise, then firm 1 will advertise a price of 5 Conditions (2) and (3) are identical to those in Narasimhan (1988) but also include the advertising cost. Because the advertising cost cancels in these expressions, the equilibrium pricing strategies are identical to those found by Narasimhan. 8

9 r, whence firm 2 could profitably advertise a price of r ε. Thus, if (h 1 r/ (h 1 + s)) (h 2 + s) < < (h 2 + s) r, then firm 2 must adopt a mixed advertising strategy as well as a mixed pricing strategy. Let β i denote the probability that firm i advertises. If firm 2 advertises with probability β 2 < 1, then firm 1 s equilibrium strategy is not clear. If h 2 + s > h 1, then for suffi ciently close to (h 2 + s) r, firm 1 would earn negative profit if it advertised the monopoly price r and did not capture the shoppers. However, as demonstrated in Proposition 1, for (h 1 r/ (h 1 + s)) (h 2 + s) < < (h 2 + s) r the equilibrium mixed advertising strategy adopted by firm 2 ensures that the probability that firm 1 captures the shoppers even when it advertises a price of r is suffi ciently high so that firm 1 always earns positive expected profit and advertises with probability β 1 = 1. Proposition 1 In a market with uniform advertising, (1) if h 1 r h 2+s, then firms advertise with probability β 1 = β 2 = 1 and employ the mixed pricing strategies defined by equations (4) and (5). Expected profits are π 1 = rh 1 and π 2 = h 1 r (h 2 + s) / (h 1 + s). (2) if h 1 r h 2+s < < (h 2 + s)r, then firm 1 advertises with probability β 1 = 1, and employs the mixed pricing strategy F 1 (p) = 0 p < / (h 2 + s), 1 h 2p and firm 2 advertises with probability β 2 = 1 pricing strategy F 2 (p) = 1 r p p p [, r), 1 p r, (6) ( ) h1 +s h 1r /rs < 1 and employs the mixed 0 p <, ()r p [, r], 1 p > r ( ) when it does advertise. Expected profits are π 1 = h1 h 2, and π 2 = 0. (3) if (h 2 + s)r (h 1 + s)r, then firm 1 advertises the reservation price r with probability β 1 = 1, firm 2 does not advertise. Expected profits are π 1 = r (h 1 + s) and π 2 = 0. (4) if > (h 1 + s)r, then neither firm advertises. (7) Proof. See appendix. 9

10 It is interesting to analyze the case when firm 2 does not advertise with probability one. We interpret the probability with which firms advertise as the intensity of advertising within a planning period as in Iyer, Soberman and Villas-Boas. We also assume that each period is independent and that there are no carry-over effects for consumers. Unlike previous models with symmetric loyal market shares in which both firms employ symmetric advertising and pricing strategies, we demonstrate how firms adopt asymmetric pricing and advertising strategy in equilibrium when loyal consumer segments differ in size. Our results stand in contrast with Iyer, Soberman and Villas-Boas in which both firms mix their advertising strategies symmetrically. Firm 1 adopts a higher advertising intensity than firm 2 in our model because firm 1 can extract more surplus from its high loyal customers upon advertising. Two features of price distributions for case (1) are noticeable, first, F 1 (r) = 1 h 2r sr. This implies F 1 (p) will have mass point at r equal to h 2r sr, which is consistent with the analysis in Narasimhan (1988). Second, F 2 (p) converges to the symmetric results analyzed by Iyer, Soberman and Villas-Boas as h 1 h 2. It is easy to check that F i (p)/ < 0 and F i (p)/ r < 0 for both firms, thus, the expected price is increasing in the advertising cost and in the buyer s reservation price, as in symmetric case. Proposition 2 In the case of uniform advertising, if < (h 2 + s) r, so that both firms advertise with positive probability, then the (random) price p 1 charged by firm 1 is first-order stochastically larger than the (random) price p 2 charged by firm 2. Proof. This follows directly from the fact that 1 F 1 (p) 1 F 2 (p) for the distributions F 1 (p) and F 2 (p) for all price p and advertising costs in the relevant ranges defined in parts (1) and (2) of proposition 1. The results of proposition 2 imply that with asymmetric loyal segments and uniform price advertising firm 2, with the smaller loyal segment, prices more aggressively than firm 1 when it does advertise. Combined with proposition 1, these results present an interesting picture of the impact of asymmetric loyal market segments on competitive advertising and pricing decisions. well known result for the symmetric case is that equilibrium profit for a firm is the maximum of the profit h i r that the firm can realize by advertising the monopoly price to its loyal segment, and the profit 0 from not advertising. Our results indicate that with asymmetric loyal market 10

11 segments firms can earn profit in excess of these amounts. In particular, if the advertising cost is low, then both firms advertise with probability 1 and firm 2 earns strictly more than the profit it would achieve by advertising the monopoly price and selling only to its loyal customers. This occurs because the larger loyal market segment of firm 1 reduces firm 1 s incentive to compete for shoppers. s a result, firm 2 adopts the more aggressive pricing strategy of the two firms, but is still able to generate profit in excess of what is earned by selling only to its loyal segment at the price r. Furthermore, firm 2 will advertise with probability 1 even if the advertising cost exceeds the revenue h 2 r that can be generated by selling to its loyal segment at the price r (for h 2 r < < h 1 r h 2+s ). Once the advertising cost increases beyond h 1 r (h 2 + s) / (h 1 + s), then firm 2 earns zero profit in equilibrium and adopts a mixed advertising strategy, where the advertising probability is decreasing in and increasing in r. This strategy applies until reaches (h 2 + s) r at which point firm 2 will cease advertising because the return does not justify the expense even if all shoppers purchase from firm 2 at the reservation price r. The results of propositions 1 and 2 also contrast starkly with the advertising and pricing behavior of firms with asymmetric market shares that compete for the shopping segment through an information gatekeeper but can sell to their loyal segment at no cost. s rnold et. al. (2011) demonstrate, in that environment the firm with the small loyal segment is more likely to advertise, but it prices less aggressively. Because loyal customers always purchase if the price does not exceed the reservation value r in the gatekeeper setting, the large firm poses more of a competitive threat. s a result, the firm with the smaller loyal segment manages the trade-off between competing through advertising frequency versus aggressive pricing by advertising aggressively but pricing less aggressively than the firm with the large loyal segment. The firm with the large loyal segment, on the other hand, limits competition in the market by advertising less intensively (has a lower probability of advertising), but it prices aggressively when it does advertise to ensure that the price reduction offered to loyal customers is justified with a high probability of capturing the shoppers. If, as in our current setting, firms must advertise to attract loyal and shopping customers alike, then the large firm has a strong incentive to advertise because advertising is required in order to capture even its loyal segment. Therefore, the large firm advertises more aggressively. However, in order to mitigate competition, it prices less aggressively than firm 2. In the symmetric model, h = h 1 = h 2, so any change in s causes the same change in h 1 and h 2. 11

12 In our asymmetric model, h 1 and h 2 are different and since F i (p) is function of two of the three market segment size variables, h 1, h 2 and s, it is possible for us to explore the effects of market segment sizes on price distributions. Our results show that expected prices for both firms increase as h 1 goes up whether h 2 goes down (s is constant) or s goes down (h 2 is constant). However, if firm 1 hold its market share h 1 constant, the expected price for firm 1 increases when s goes up (h 2 goes down) and decreases when s goes down (h 2 goes up). When s goes up holding h 1 constant, the lowest price firm 2 charges does not change, while the lowest price firm 1 charges goes down. This gives firm 1 more incentive to charge a higher price. s a result, the expected price for firm 1 increases when s goes up (h 2 goes down). Table 1: Market segment sizes effect on price for uniform advertising h 1 h 2 s F 1 F s suggested by intuition, β < 0 and β r > 0, so firm 2 s advertising probability is decreasing with advertising cost and increasing with reservation price. The relation between β and s is more interesting. Firm 2 will advertise less if the increased shoppers are from its loyal segment, h 2. However, if the increased shopper are coming from firm 1 s loyal segment, h 1, it advertises more only when h 1 > h 2 + s. Basically, there are two effects when shoppers increase. First,it increases the fraction of firm 2 s demand that it has to compete with firm 1, which lowers its advertising frequency. Second, it increases total demand available to firm 2 when it is price is lower than firm 1,which increases its frequency to advertise. In case when increased shoppers are from its loyal segment, the second effect disappears, so firm 2 will advertise less. However, if increased shoppers are from h 1, Firm 2 will advertise more only if the first effect dominated by the second effect, which is when h 2 + s is less than h 1. 12

13 2.2 Targeted dvertising with Uniform Prices We now analyze firms advertising and pricing behavior when firms have the ability to target particular segments of the market. In contrast to the case of uniform advertising in which the firm advertises to the entire market at a cost of, we now assume that an individual segment h i, or s can be reached at a cost of h i or s. In this setting a given firm i would never advertise to the segment h j of consumers loyal to the rival firm. Furthermore, firm i can achieved a profit of π i = h i (r ) by advertising only to its own loyal segment. With targeted advertising, a firm will always advertise to its own loyal segment provided < r, while if > r, then neither firm would ever choose to advertise. For the remainder of the analysis, we assume < r. We also assume that while firms can selectively choose to advertise to only its own loyal customers, or to both its loyal customers and the share s of shoppers in the market, the firm is not able to price discriminate between these two segments. We maintain our assumption that h 1 > h 2. Proposition 3 Suppose that both firms can target their advertising to ecific segments of the market. Then in equilibrium, with probability β 1 = ( 1 ) h2 + s r h 1 + s firm 1 advertises to both its own loyal segment h 1 and the shopping segment s and adopts the mixed pricing strategy F 1 (p) = 0 p < h 1r+s, 1 h 1r+s r p (r )s p h 1 r+s p r, 1 p > r, and with probability 1 β 1 firm 1 advertises the price r to its loyal segment h 1 only; with probability β 2 = 1 firm 2 advertises to both its loyal segment h 2 and the shopping segment s and adopts the mixed pricing strategy F 2 (p) = 1 + h 1 s 0 p < h 1r+s, h 1r+s h 1 r+s p < r, 1 p r. 13

14 The equilibrium profits are π 1 = h 1 (r ) and π 2 = ( h 1r+s )(h 2 + s) = h 1 (r ) h 2+s. Proof. See appendix. Under uniform advertising, the lowest price p 1 that firm 1 is willing to advertise is less than that of firm 2 because firm 1 has a larger consumer base to assume the advertising cost. However, under targeted advertising, firm 1 is less willing to lower its price in order to compete for comparison shoppers because it can extract more surplus by targeting its loyal consumers. s a result, when both firms are able to target their advertising, the lowest price p 2 that firm 2, with the smaller loyal share, is willing to charge is less than that of firm 1. By standard arguments, advertising to both its loyal segment and the shoppers is firm 2 s strictly dominant strategy. Proposition 4 In the case of targeted advertising with uniform pricing, if < r, so that both firms advertise with positive probability in equilibrium, then the (random) price p 2 charged by firm 2 is first-order stochastically larger than the (random) price p 1 charged by firm 1. The expected price increases with both reservation price r and advertising cost as before. We also have similar asymmetric market segment effects on pricing. The expected prices for both firms decrease as h 1 increases regardless of whether h 2 decreases (and s remains constant) or s decreases (and h 2 remains constant). Similarly, the expected prices for both firms increase as h 1 decreases regardless of whether h 2 increases (and s is constant) or s increases (and h 2 is constant). However, if h 1 is held constant, both firms expected price increase when s increases (and h 2 decreases) and decrease when s decreases (and h 2 increases). Explanations for these results are similar to the case of uniform advertising except that firm 1 and firm 2 have switched their roles. Table 2: Market segment sizes effect on price for targeted advertising h 1 h 2 s F 1 F Similar to β 2 in the case of uniform advertising, with targeted advertising, firm 1 s equilibrium advertising probability β 1, is decreasing with advertising cost and increasing with reservation price. 14

15 Firm 1 will advertise less if the increased shoppers are from its loyal segment, h 1. However, in contrast to the uniform advertising case, where firm 2 advertise less than firm 1 only if is suffi ciently large, with targeted advertising firm 1 will always advertise less even when the increased shoppers are from its competitor s loyal segment h 2. Because firm 1 cannot price discriminate between shoppers and its loyal consumers, the gain from lowering its price to capture shoppers is always less than the loss from cutting the price for its loyal consumers. By the same reasoning, firm 1 will advertise less if h 1 goes up and h 2 goes down (holding s constant). gain, if we consider a monopolist advertising firm, the optimal advertising fee is = r. The profit r(+h 2 ) from charging an advertising fee of r is greater than the profit (h 2 + s + h 1 + β 1 s) that can be achieved from any < r. Firm 1 advertises the price r to its loyal segment only, and firm 2 advertises r to both its loyal segment and the shoppers with probability 1. Both firms earn 0 profit when both firms have the ability to target advertising. monopolist advertising firm would extract all available surplus in the market. 2.3 Large firm adopts targeted advertising and small firm adopts uniform advertising Given the ability to target advertising, firm 1 would eliminate its wasted advertising cost on those consumers who only consider buying products from firm 2. Firm 2, on the other hand, pays an advertising cost and reaches the entire market if it advertises. Proposition 5 Suppose that firm 1 has the ability to target its advertising while firm 2 is limited to uniform advertising. Then (1) if < h 2+s 1+s r, then with probability β 1 = h 2+s and shoppers and employs the mixed pricing strategies r r firm 1 advertises to both its loyal segment F 1 (p) = 1 β 1 (1 h 1 r+s (h 2 + s) h 2 p ) = r ( 1 + h 1 r s h ) 1r + s for p [ h 1r + s, r], (8) h 1 + s and with probability 1 β 1, firm 1 advertises a price r to to its loyal segment only; and firm 2 advertises to the whole market with probability β 2 = 1 and employs the mixed pricing strategy F 2 (p) = 1 + h 1 s h 1r + s 15 for p [ h 1r + s, r]. (9) h 1 + s

16 ( ) Equilibrium profits are π 1 = h 1 (r ) and π 2 = (h 2 + s) h1 r+s. (2) if [ h 2+s 1+s r, (h 2 + s)r], then firm 1 advertises to both its loyal segment and shoppers with probability β 1 = 1 and employs the mixed pricing strategy F 1 (p) = 1 ph 2 for p [, r], (10) h 2 + s and with probability β 2 pricing strategy = (h 2+s)r rs firm 2 advertises (uniformly) and employs the mixed F 2 (p) = 1 (1 (h 1 + s)(1 + h 1 ) h 1p (r p) ) = 1 β 2 ((h 2 + s) r ) p for p [, r], (11) h 2 + s and with probability 1 β 2 firm 2 does not advertise. Equilibrium profits are π 1 = h 1 and π 2 = 0. (3) if (h 2 + s)r < < r, firm 1 advertises the price r to both its loyal segment and shoppers with probability β 1 = 1, and firm 2 does not advertise. Equilibrium profits are π 1 = (h 1 + s)(r ) and π 2 = 0. Proof. See appendix. Notice that firm 1 always advertises to its loyal consumers as long as < r because it has the ability to target ecific segments, however firm 2 adopts a mixed advertising strategy when the advertising cost is relatively high because it is unable to target its ads. The mixed advertising strategy by firm 2 reduces competition in price for the shoppers by firm 1. This enables firm 2 to price less competitively which raises firm 2 s expected revenues by an amount just suffi cient to cover the increased advertising cost. 2.4 Large firm adopts uniform advertising and small firm adopts target advertising Suppose that only the small firm 2 has the ability to target advertising. s usual, our equilibrium results depend on the level of advertising cost. Proposition 6 Suppose that firm 2 has the ability to target its advertising while firm 1 is limited to uniform advertising. 16

17 (1) If < (h 1 h 2 )r, then firm 1 advertises (uniformly) with probability β 1 = 1 and employs the mixed pricing strategy F 1 (p) = 1 + h 2 s (h 2 + s) h 1 r (h 1 + s) for p [ h 1 r, r], (12) h 1 + s and firm 2 advertises to both its loyal segment and shoppers with probability β 2 = 1 and employs the mixed pricing strategy F 2 (p) = 1 h 1(r p) h 1 r for p [, r]. (13) h 1 + s Equilibrium profits are π 1 = h 1 r and π 2 = ( h 1r )(h 2 + s). (2) If [ (h 1 h 2 )r, h 1+s 1+s r], then firm 1 advertises with probability β 1 = 1 using the mixed pricing strategy with probability β 2 = h 1+s r r mixed pricing strategy F 1 (p) = 1 h 2r + s ph 2 ps for p [ h 2r + s, r]; (14) h 2 + s firm 2 advertises to both its loyal segment and shoppers using the F 2 (p) = (r ) rs (h 2 + s) (r p) r (r ) for p [ h 2r + s h 2 + s, r], and with probability 1 β 2 firm 2 advertises the price r to its loyal segment only. Equilibrium profits are π 1 = (h 1 + s) h 2r+s and π 2 = h 2 (r ), reectively; (3) [ h 1+s 1+s r, (h 1 + s)r], firm 1 advertises with probability β 1 = (h 2+s)(h 1 r +rs) (s+h 1 )rs mixed pricing strategy using the F 1 (p) = (h 1 + s) rp r (h 1 + s) rp p for p [, r]; (15) h 1 + s firm 2 advertises to its loyal segment and shoppers with probability β 2 = 1 using the mixed pricing strategy F 2 (p) = 1 h 1p for p [ h 1 + s, r]. Equilibrium profits are π 1 = 0 and π 2 = (h 2 + s)( ) = h 2(). (4) [(h 1 + s) r, r], firm 1 does not advertise, and firm 2 advertises the price r to its loyal segment and shoppers with probability β 2 = 1, and firm profits are π 1 = 0, and π 2 = (h 2 + s) (r ). 17

18 Proof. See appendix. 3 Concluding remarks In this paper,we analyze duopoly advertising and pricing strategies with asymmetrical loyal consumers. We extend results of Narasimhan showing that in a market with informative advertising and asymmetric loyal market shares firms not only price asymmetrically but also advertise asymmetrically. When firms have asymmetric loyal customer shares, the nature of advertising competition is critical to determining optimal advertising and pricing strategies. Firms can balance the incentive to compete in price by competing less intensively in advertising. Similarly, a firm can successfully advertise to expand its market if it prices less aggressively (i.e., by adopting a puppy dog strategy). However, whether a firm should advertise intensely and price cautiously or price aggressively and advertise cautiously depends on the advertising mechanism available. If firms are limited to uniform advertising strategies, then the firm with the larger loyal market will advertise more aggressively and price less competitively than the firm with the smaller loyal market share. These results are reversed if both firms are able to implement targeted advertising strategies. 18

19 4 ppendix Proof of Proposition 1. The equilibrium strategies for h 1r (h 2 + s) and > (h 2 + s) r were verified in the paragraph preceding Proposition 1. lso note that the minimum price that firm 2 would ever advertise must satisfy p 2 (h 2 + s) 0, or p 2 / (h 2 + s). Because firm 1 can capture all shoppers by advertising p 2, firm 1 s profit satisfies π 1 (h 1 + s) = (h 1 h 2 ) > 0, so firm 1 will advertise with probability β 1 = 1 in any equilibrium in which it is optimal for firm 2 to advertise. Now consider the case of h 1 r (h 2 + s) < < (h 2 + s) r. First note that there is no equilibrium in which firm 2 does not advertise. If firm 2 did not advertise, then firm 1 would advertise r and get a share h 1 + s of the consumers. However, if firm 1 advertises r, then firm 2 could advertise r ε and sell to the share h 2 + s of consumers and earn a profit of π 2 = (r ε) (h 2 s) > 0 for ε > 0 suffi ciently small. Similarly, if β 2 = 1, then the pricing strategies (4) and (5) imply π 2 < 0 if > h 1r (h 2 + s). Therefore, 0 < β 2 < 1 must hold in any equilibrium with h 1r (h 2 + s) < < (h 2 + s) r, and, if β 2 (0, 1), then π 2 = 0. (If π 2 > 0, then β 2 = 1 is optimal and if π 2 < 0, then β 2 = 0 is optimal.) Because firm 1 advertises with probability β 1 = 1, and π 2 = 0, firm 1 s equilibrium mixed pricing strategy must satisfy h 2 p + (1 F 1 (p)) = 0 (16) for any p [p, r), which implies F 1 (p) = 1 h 2p. Setting F 1 ( p ) = 0 yields p = p2 = r (h 2 + s) by assumption., and F 1 (r) = (r (h 2 + s) ) /rs > 0 because < This implies firm 1 s equilibrium mixed pricing strategy has a mass point at r. Because firm 1 can capture the share h 1 + s of customers by advertising p, firm 2 s equilibrium advertising and pricing strategies must satisfy p (h 1 + (1 β 2 )s + β 2 (1 F 2 (p))s) = h 2 + s (h 1 + s) (17) for any p [p, r). Noting that at most one firm s equilibrium pricing strategy can have a mass ( ) point at r, so F 2 (r) = 1, and evaluating equation (17) at p = r yields β 2 = 1 h1 +s h 1r /rs. ( ) Substituting this expression for β 2 into equation (17) yields F 2 (p) = 1 r p p. Finally, 19 (1 h 1 )r

20 setting F 2 ( p ) = 0 yields p = Proof of Proposition 3.. Profit for firm i from advertising only to its loyal segment is h i (r ).Firm i will advertise to both its loyal segment and the shoppers if (h i + s) ( p ) h i (r ) or p rh i + s h i + s. This implies p 1 h 1r+s, so the lowest profit firm 2 can earn by advertising to its loyal segment and the shoppers is ( ) h1 r + s h 2 + s (h 2 + s) = h 1 h 1 + s h 1 + s (r ) > h 2 (r ) because r > and h 1 > h 2 by assumption. Because firm 2 earns strictly greater profit by advertising to both its loyal segment and the shoppers than by advertising to its loyal segment alone, β 2 = 1. Given β 2 = 1, the expected profit firm 1 achieves by advertising any price p in the support of its mixed pricing strategy to both its loyal segment and the shoppers must equal the profit h 1 (r ) it can achieve by advertising r to its loyal segment alone. This implies firm 2 s equilibrium mixed pricing strategy must satisfy p (h 1 + (1 F 2 (p))s) (h 1 + s) = h 1 (r ) (18) which implies F 2 (p) = 1 + h 1 s h 1r + s. ( ) Setting F 2 p = 0 yields p = h 1 r+s. Notice that F 2(p) has a mass point of magnitude /r at the monopoly price r. Given p = h 1r+s, firm 2 s expected profit from advertising p to its loyal segment ) and the shoppers is (h 2 + s). Equating this expected return with firm 2 s expected ( h1 r+s return from advertising any price p implies that firm 1 s equilibrium advertising and mixed pricing strategies must satisfy p (h 2 + (1 β 1 )s + β 1 (1 F 1 (p))s) (h 2 + s) = ( h1 r + s h 1 + s ) (h 2 + s). (19) 20

21 Noting that F 1 (r) = 1 and evaluating equation (19) at p = r yields β 1 = ( 1 ) h2 + s r h 1 + s. Substituting this expression for β 1 into (19) yields F 1 (p) = 1 h 1r + s r p s(r ) p. ( ) Setting F 1 p = 0 yields p = h 1 r+s. Thus, the equilibrium mixed pricing strategies are defined by F 1 and F 2, firm 2 advertises with probability β 2 = 1, and firm 1 advertises with probability β 1 < 1. Proof of Proposition 5. Firm 1 can earn h 1 (r ) by targeting its loyal customers, so the lowest price p 1 that firm 1 will ever advertise to shoppers satisfies h 1 (r ) = ()p 1 () ( ) or p 1 = h 1r+s. Given this price, firm 2 must earn at least () h1 r+s in any equilibrium. This return is strictly positive if < h 2+s 1+s r. Thus, if < h 2+s 1+s r, then firm 2 earns a strictly greater profit by advertising than by not advertising, so β 2 = 1. Given β 2 = 1, the expected profit firm 1 achieves by advertising any price p in the support of its mixed pricing strategy to both its loyal segment and the shoppers must equal the profit h 1 (r ) it can achieve by advertising r to its loyal segment alone. This implies firm 2 s equilibrium mixed pricing strategy must satisfy p (h 1 + (1 F 2 (p))s) (h 1 + s) = h 1 (r ) (20) which implies F 2 (p) = 1 + h 1 s h 1r + s. ( ) Setting F 2 p = 0 yields p = h 1 r+s. Because firm 2 earns a positive expected profit from advertising (and a profit of 0 by not advertising), the equilibrium pricing and advertising strategies of firm 1 must ensure that firm 2 earns the same expected profit from any price it advertises which implies h 1 r + s h 1 + s (h 2 + s) = p (h 2 + s (1 β 1 F 1 (p))). (21) or F 1 (p) = 1 β 1 (1 h 1 r+s (h 2+s) ph 2 ps ). Noting that firm 2 s equilibrium pricing strategy has a mass 21

22 point at r, so F 1 (r) = 1, and substituting p = r into equation (21) yields β 1 = 1 r(h 1 h 2 )+() ()r. The resulting equilibrium profits are π 1 = h 1 (r ) and π 2 = h 1r+s (h 2 + s). If h 2+s 1+s r < < (h 2 + s)r, then firm 2 would achieve a negative expected return from the strategies above, so the minimum price firm 2 would advertise equates the profit (h 2 + s)p 2 from advertising the minimum price with the profit of 0 from not advertising. This implies p 2 = which is greater than the minimum price p 1 = h 1r+s the price p 2 = that firm 1 would ever charge. By advertising to its loyal segment and the shopping customers firm 1 can achieve an expected profit of (h 1 + s) (/ (h 2 + s) ) = (h 1 + s) h 1 / (h 2 + s) > (h 1+s)h 1 r 1+s > h 1 (r ) where the two inequalities follow from the fact that > h 2+s 1+s r. Because h 1 (r ) is the profit firm 1 achieves by advertising only to its loyal segment, firm 1 will advertise to its loyal segment and the shoppers with probability β 1 = 1. Given β 1 = 1, the expected profit firm 2 achieves by advertising any price p in the support of its mixed pricing strategy must equal the profit of 0 it can achieve by not advertising. This implies firm 1 s equilibrium mixed pricing strategy must satisfy p (h 2 + (1 F 1 (p))s) = 0 (22) or F 1 (p) = p(h 2+s). Setting F 1 ( p ) = 0 implies p = = p 2. Similarly, because β 1 = 1, any price firm 1 advertises must satisfy ( ) (h 1 + s) h 2 + s = p (h 1 + s (1 β 2 F 2 (p))) (h 1 + s) ( ) which implies F 2 (p) = 1 h1 +s β 2 (h 2p + ). Noting that firm 1 s equilibrium pricing strategy has a mass point at r, so F 2 (r) = 1, implies β 2 = 1 rs ((h 2 + s) r ). The resulting equilibrium ( ) profits are π 1 = (h 1 + s) and π 2 = 0. Finally, if (h 2 + s)r < < r, then firm 2 will not advertise, and firm 1 advertises to its loyal customers and shoppers with probability β 1 = 1 and charges r in equilibrium. Proof of Proposition 6 The proof is similar to the proof of Proposition 5 with the roles of firms 1 and 2 reversed. Firm 2 can earn h 2 (r ) by targeted advertising to its loyal customers only, so the lowest price p 2 that firm 2 will ever advertise to shoppers satisfies h 2 (r ) = (h 2 + s)p 2 (h 2 + s) (23) 22

23 ( ) or p 2 = h 2r+s. Given this price, firm 1 must earn at least () h2 r+s in any equilibrium. This return is strictly positive if < h 1+s 1+s r. Thus, if < h 1+s 1+s r, then firm 1 earns a strictly greater profit by advertising than by not advertising, so β 1 = 1. Similarly, the lowest price firm 1 will ever advertise satisfies 6 h1r (h1 + s) p 1 or p 1 h 1 r/ (h 1 + s). It follows that if < (h 1 h 2 )rs, then p 1 > p 2 and firm 2 is strictly better off targeting both loyal and shopping customers than targeting loyal customers only, so β 2 = 1 ssume < (h 1 h 2 )rs, so β 1 = β 2 = 1. Then firm 1 s equilibrium pricing strategy must satisfy p (h 2 + (1 F 1 (p))s) (h 2 + s) = p (h 2 + s) (h 2 + s). (24) Suppose that F 1 (r) = 1. Then equation (24)implies p = h 2 r/ (h 2 + s) < p 2 which can not occur. It follows that F 1 (r) < 1, so firm 1 s strategy has a mass point at r and F 2 (r) = 1. Given F 2 (r) = 1, firm 2 s equilibrium pricing strategy must satisfy p (h 1 + s (1 F 2 (p))) = h 1 r which implies F 2 (p) = 1 h 1 (r p). ps Setting F 2 (p) = 0 implies p = h 1 r/ (h 1 + s). Substituting this value for p into equation (24) yields F 1 (p) = 1 + h 2 s h 1r (h 2 + s) (h 1 + s) ps. Setting F 1 ( p ) = 0 yields p = h1 r/ (h 1 + s). Firm profits are π 1 = h 1 r and π 2 = h 2+s (h 1 (r ) s). Now assume (h 1 h 2 )rs < h 1+s 1+s r. Note that β 1 = 1 still applies, so equation (24), and consequently F 1 (r) < 1 and F 2 (r) = 1, must still hold in equilibrium. However, it is no longer 6 Note that this equation does not necessarily hold with strict equality because the probability β 2 that firm 2 advertises impacts firm 1 s expected return from (uniformly) advertising the price r, and it is possible that β 2 < 1. 23

24 necessary that β 2 = 1, so firm 2 s equilibrium pricing and advertising strategies must satisfy p (h 1 + s (1 β 2 F 2 (p))) = r (h 1 + (1 β 2 ) s) (25) which implies F 2 (p) = β 2rs (h 1 + s) (r p). β 2 To determine the equilibrium values for p and β 2, first note that p p 2 = h 2r+s. Suppose p > h 2r+s. This can only occur if p 1 > p 2 which implies the equilibrium values of p and β 2 satisfying equation (25) result in p > h 2r+s. Evaluating (25) at p implies p = r rsβ 2 () greater than h 2r+s r(h 1 h 2 ) if and only if β 2 < (r )(h 1+s) r() which is 1 where the second inequality follows from. However, if p > h 2r+s, then β 2 = 1 is optimal for firm 2. But β 2 = 1 implies p = h 1 r/ (h 1 + s) < p 2, a contradiction. Thus, p h 2r+s never establish a minimum price less than h 2r+s, it follows that p = h 2r+s in equilibrium. Using these equilibrium values for p and β 2 implies in equilibrium. Because firm 2 will and β 2 = (r )(h 1+s) ()r F 1 (p) = s (p ) h 2 (r p), ps and F 2 (p) = (r ) rs r (h 2 + s) (r p). (r ) It is easy to verify that these are well defined cumulative distribution functions for p [ h 2r+s, r] and that firm 1 s strategy has a mass point of 1 /rs at p = r. The resulting equilibrium profits are π 1 = h 1 (r ) and π 2 = h 2r+s (h 2 + s) = h 2 r (1 s). ssume h 1+s 1+s r < < (h 1 + s)r. Note that p 1 must satisfy p 1 (h 1 + s) 0, so p / (h 1 + s), and > h 1+s 1+s r implies / (h 1 + s) > h 2r+s = p 2.This implies firm 2 earns a strictly greater profit by targeting shoppers and its loyal customers at the price p than by targeting its loyal customers alone, so β 2 = 1. Given β 2 = 1, the equilibrium pricing strategy for firm 2 must satisfy p (h 1 + s (1 F 2 (p))) = (h 1 + s)p, so F 2 (p) = (h 1+s)(p p) ps. Suppose F 2 (r) = 1. Then p = rh 1 / (h 1 + s) < / (h 1 + s), where the inequality follows from > h 1+s 1+s r, which contradicts p / (h 1 + s). Thus, F 2 (r) < 1 and F 1 (r) = 1 in equilibrium. Next, note that firm 24