Competition, Reputation and Compliance
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Vanin, Paolo Working Paper Competition, Reputation and Compliance Quaderni - Working Paper DSE, No. 682 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Vanin, Paolo (2009) : Competition, Reputation and Compliance, Quaderni - Working Paper DSE, No. 682, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4562 This Version is available at: https://hdl.handle.net/10419/159523 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/
Competition, Reputation and Compliance∗ Paolo Vanin† November 13, 2009 Abstract This paper displays a linear demand oligopoly model, in which firms endogenously decide whether to enter the market and whether to specialize on high or low quality products, and then repeatedly interact to sell experience goods. It shows that the intuition that low and rising prices grant compliance with quality promises extends to this setting, provided that high quality is sufficiently important to buyers. JEL-Classification: L13, L14, L15 Key-words: Oligopoly, Quality, Price Signals, Consumers’ Trust ∗I would like to thank Heski Bar-Isaac, Antonio Cabrales, Matteo Cervellati, Sjaak Hurkens, Doh-Shin Jeon, Jos´e Luis Moraga-Gonz´alez, Joel Shapiro, Yaron Yehezkel and seminar participants at Pompeu Fabra University and University of Padova for useful discussions. I also benefited from comments from conference participants at EDP Jamboree in Louvain, EEA-ESEM in Budapest, EARIE in Valencia and ASSET in Padova. A previous version of this article appeared as a chapter in my Ph.D. dissertation at UPF. †Department of Economics, Universit`a di Bologna; e-mail: [email protected] 1
1 Introduction Klein and Leffler (1981) suggest a mechanism through which reputation may provide the adequate incentive for sellers of experience goods to comply with promises (e.g., supply high quality). If buyers pay a price premium for high quality, if they are informed on past compliance and never buy from a seller who cheated on quality in the past, the present value of the stream of future profits granted by compliance may be higher than the one period deviation gain that can be obtained by cheating consumers, so that the seller is indeed induced to be trustworthy. Shapiro (1983) formally investigates this mechanism and shows that low and rising prices guarantee high quality in a competitive market, because premiums for high quality ensure that no firm has an incentive to cut on quality and cheat the market, but competition for such premiums induces firms to set initially low, loss-making prices, which correspond to an investment in reputation, to which later profits are the normal market return. The degree of market competition may be fundamental to determine incentives for high quality provision. Competition may both lower monopoly rents, and thus reduce returns from promise compliance, and offer buyers more alternatives, and thus strengthen punishments for non compliance. Competition itself depends on entry and exit, which depend on expected profits and therefore on returns to reputation and on reputation building costs (besides standard entry and exit costs). If the number of entrants is limited, strategic interaction, which is assumed away in competitive models with infinitely many firms, is likely to play a major role. This paper investigates how reputation works in a market in which the number of firms is endogenous, quality is a long lasting choice variable and low quality would not be bought (at profitable prices) if recognized as such. Specifically, I consider a game with four stages: entry, quality selection (of an experience good) and twice repeated market interaction (repetition allows for reputation accumulation). I show that the intuition that low and rising prices grant high quality provision extends to the present oligopolistic setting, provided that high quality is sufficiently important for buyers.1 This work is related to the literature on price signals of quality, in which 1In a companion paper (Vanin, 2009), to which I refer for a deeper discussion of the literature and of the model’s details, I show that, if high quality is less important to buyers, then the reputation mechanism fails, giving rise to interesting market dynamics with equilibrium cheating. 2
market structure and quality are assumed as exogenously given.2Yet it is more closely related to the small recent literature that investigates reputation together with entry and quality choice.3In particular, H¨orner (2002) presents a dynamic version of Klein and Leffler (1981), in which firms enter the market, choose quality every period and use prices to signal quality. Each firm’s (quality guaranteeing) price rises over time (as its reputation increases), until bad luck drives it out of the market. Consumers’ knowledge of a firm’s customer base implies that it cannot raise its price to mimic higher reputation firms. My assumption that buyers would not purchase low quality at profitable prices under perfect information has the opposite implication that upwards price mimicry is feasible. Indeed, it is often the case that buyers ignore at the same time sellers’ quality and their customer base. Besides for this aspect, the present work also differs from H¨orner (2002) because it explicitly considers strategic interaction, rather than featuring a constant continuous mass of firms on the market. Toth (2008) presents a dynamic oligopoly model with stochastic entry and with investment in quality every period, and shows that market concentration may alleviate moral hazard. Yet his work is focused on firms’ survival contest and does not present an explicit model of market interaction (in particular, prices are not used as signals of quality). My contribution consists precisely in providing an explicit analysis of dynamic market interaction, allowing prices to serve as signals of quality. Moreover, I also differ from these models in that I consider quality as a long-lasting choice variable, which increases marginal costs, rather than as a variable chosen made every period. To the extent that product quality depends on the skills of a firm’s employees, as is the case in many service markets, this view appears plausible and worth investigating. The remainder of the paper is organized as follows. Section 2 presents the model, Section 3 analyzes its equilibrium and Section 4 concludes. A technical lemma is presented in Appendix. 2See, among others, Milgrom and Roberts (1986) and Bagwell and Riordan (1991) for monopoly; Hertzendorf and Overgaard (2001), Fluet and Garella (2002), Yehezkel (2008) and Daughety and Reinganum (2007) for duopoly; Daughety and Reinganum (2008) for an n-firm oligopoly; and Allen (1984) and Cooper and Ross (1984) for competitive models with U-shaped average cost function (I maintain the assumption of constant returns to scale). 3Overgaard (1994) considers a monopolist with a potential entrant and Bester (1998) investigates a duopoly with both quality and location choice on a line. My work is complementary to the latter, because I endogenize the number of firms, taking as given the degree of horizontal differentiation. 3
2 Model 2.1 Structure I consider a game with the following four-stage structure. At stage one an infinite number of potential entrants simultaneously decide whether to enter the market or not. Each entering firm pays a fixed entry cost ζ > 0, which is sunk after entry, and chooses a different variety of an experience good. Varieties are imperfect substitutes. The number of firms who enter the market is denoted by n. At stage two the nfirms on the market simultaneously choose whether to produce high or low quality. The result of these choices is a vector z∈ {0,1}n, with zj= 1 meaning that firm jhas chosen high quality. Denote h=Pn j=1 zjthe number of high quality firms. Once decided, the quality level remains the same in the two following market stages. To simplify and concentrate only on asymmetric information on consumers’ side, I assume that, once chosen, a firm’s quality becomes known to all firms on the market, but not to consumers. Consumers may learn a firm’s quality either through direct experience with its products or by information extraction from equilibrium price signals. At stage three firms and consumers interact on the market for the first time. They move sequentially: first, firms simultaneously choose prices, determining a price vector p1∈Rn +. Next, having observed p1, consumers (indeed, a representative consumer) decide how much to demand to each firm, determining the demand vector q1∈Rn +. Stage four is analogous to stage three, but consumers now have additional information: if they have consumed a positive quantity of a firm’s product, they are fully informed about its quality. Again, first firms simultaneously choose prices and determine the new price vector p2∈Rn +and then consumers choose the new demand vector q2∈Rn +. 2.2 Preferences and technology Preferences are assumed in such a way as to generate a linear demand for each product:4 4The model first presented by Shubik and Levitan (1980) and more recently used by Motta (2004) is extended by allowing for imperfect observability and product-specific quality, yielding the following expected utility function: U(q,e) = Pn j=1 α(ej)qj− n 2(1+µ)Pn j=1 q2 j+µ nPn j=1 qj2. See Vanin (2009) for a derivation of (1). 4
qj(p,e, n) = 1 n(n+µ(n−1) n[α(ej)−pj]−µ nX i6=j [α(ek)−pk]),(1) or, in matrix notation, q(p,e, n) = E(n)·[α(e)−p], where E(n) is an n×n matrix with elements Eii(n) = n+µ(n−1) n2and Eik(n) = −µ n2;pis the price vector; e∈[0,1]nis a vector of beliefs, i.e., its elements are the probability attributed by the representative consumer to the fact that each good is of high quality, conditional on information about previous play of the game (which I omit to write for notational simplicity): ej= Pr{zj= 1};α(ej) reflects the utility value attributed to good j’s expected quality, defined as α(ej) = β+ejγ, where β≥0 and γ≥0 are parameters: βcaptures the value attributed to a unit of a low quality good and γthe additional value of high over low quality; α(e) is the vector of α(ej)’s; µ∈[0,∞) is a parameter capturing the degree of substitutability between different varieties; yis a perfectly competitive outside good, introduced only to make partial equilibrium analysis justified. One feature of this model is that (at interior consumers’ choices) market size, Q(p,e, n)≡Pn j=1 qj(p,e, n) = 1 nPn j=1[α(ej)−pj] = ¯α−¯p, does not depend upon either the degree of substitutability or the number of products, but only upon average expected quality and average price. In the special case in which all products are expected to be of the same quality α(e) and have the same price p, individual demands are simply qj= α(e)−p n. Identical firms with constant returns to scale and marginal cost c < α(e) react to this demand by setting the Nash equilibrium price pE(n, e, c) = nα(e)+[n+µ(n−1)]c 2n+µ(n−1) ,(2) which is increasing in eand c, decreasing in nand µ, converges to cas µ→ ∞ and further simplifies to the usual monopoly price α(e)+c 2if n= 1. To later consider deviations from equilibrium, notice that if firm jmanages to convince consumers that it is the only one offering high quality, i.e., if ej= 1 and ∀i6=j, ei= 0, then ∀n > 0 and ∀psuch that pj< α(1) and pi≥α(0) ∀i6=j, it holds that qj(p,e, n) = 1+µ n+µ[α(1) −pj] and ∀i6=j, qi(p,e, n)=05. 5The reason why firm j’s demand depends on nis that, although jis the only one 5
All goods are produced with a constant returns to scale technology, with higher quality being more expensive to produce. Marginal costs of low and high quality are cL≥0 and cH> cL, respectively. Firms are assumed to exit the market whenever they expect non positive profits. 2.3 Equilibrium concept and parameter restrictions I look for a pure strategy weak perfect Bayesian equilibrium (WPBE) of the entire game and restrict attention to equilibria that are symmetric, in the sense that all firms choosing the same quality also set the same price. Since several equilibria are possible, depending on how consumers form quality expectations based on observed prices, and on how firms use prices to signal (or hide) their quality, I restrict attention to a simple class of belief functions (specified below), characterized by the fact that consumers distrust price signals whenever they are easy to imitate, and to ‘investment in reputation’ introductory prices, by which high quality firms signal their quality through initially low, loss-making prices, which are too low to be profitably imitated by low quality firms. Two assumptions are maintained throughout the analysis and are introduced and discussed here. Let ˆγ≡µ2+6(1+µ)+(2+µ)√µ2+8(1+µ) 2(1+µ)(cH−cL).6 Assumption 1. α(0) = cL Assumption 2. γ≥ˆγ Under perfect information, Assumption 1, which equalizes the intrinsic utility of low quality goods and their production cost, makes demand for low quality goods insufficient even for the profitable entry of a single low quality monopolist, since its demand would be positive only at prices strictly below selling a positive quantity, it is not the only one initially on the market. Consumers are ‘tempted’ by the other goods, although they do not buy them: the presence of other firms posting prices and offering their products reduces the marginal utility derived from j’s good, so that jis able to sell at pja lower quantity than it would, at the same price, if it were alone on the market (i.e., if n= 1). Technically, only j’s FOC holds with equality, whereas all the other ones hold with strict inequality (see Vanin, 2009). Notice that, given n > 1 and p,j’s demand increases in µ, since a higher degree of substitutability reduces consumers’ temptation from different goods. 6The technical origin of ˆγis made clear in the proof of Lemma 1 in the Appendix. Notice that ˆγis unboundedly increasing both in µand in (cH−cL). 6
marginal cost. This implies that, under imperfect information, firms can profitably produce goods only as long as they manage to convince consumers of their high quality (or count to recoup initial losses in the future). It also implies that separation (of high from low quality firms) through upward distorted prices is impossible, because, if any price above cLwere a credible signal of high quality, it would be imitated by low quality firms, thus losing its credibility. Assumption 2 grants that, if high quality firms separate from low quality ones by setting initial prices at cL, then future profits from repeated purchase always compensate initial losses, thus making full high quality provision possible.7 If recognized as such, low quality firms leave the market, whereas high quality firms stay on the market and price according to (2). This is reflected in the full information equilibrium at stage 4. By the same logic, it is impossible that at stage 3 both high and low quality firms stay on the market and set two different prices, thus being recognized as such. This justifies the focus on beliefs that support equilibria with pooling prices. If high quality firms are able to separate themselves from low quality ones through low prices, then the market dries up for low quality firms, and these are forced out of the market, implying that nobody at stage 2 would choose low quality. This is precisely what Assumption 2 grants. The effects of distrust and of investment in reputation on quality choice are discussed in Propositions 1 and 2. Entry costs then determine the number of entrants, thus closing the model and allowing to make comparative statics exercises (Proposition 3). In what follows I make these ideas precise. I order firms on the market by assigning lower indices to high quality ones. I start solving the model by backward induction, establishing sequential rationality of strategies and deferring to the end the consistency requirement between beliefs and strategies along the equilibrium path of play. 7It also implies that γ > cH−cL, which, given Assumption 1, is equivalent to α(1) > cH, which ensures that high quality firms receive positive demand in equilibrium and also makes high quality provision socially efficient. 7
3 Analysis 3.1 Stage 4: second market interaction When consumers choose demand in the last move before the game ends, they are fully informed about the quality of goods on the market.8All low quality firms exit the market. High quality firms set prices, sell quantities and make profits according to (3), (4) and (5), respectively:9 p2(h) = hα(1) + [h+µ(h−1)]cH 2h+µ(h−1) ,(3) q2(h) = h+µ(h−1) h[2h+µ(h−1)][α(1) −cH],(4) π2(h) = h+µ(h−1) [2h+µ(h−1)]2[α(1) −cH]2.(5) 3.2 Stage 3: first market interaction At stage 3 (first market interaction) firms set prices p1, consumers observe them, formulate beliefs on each firm’s quality and then choose demand.10 There exists no pure strategy weak perfect Bayesian equilibrium in which, along the equilibrium path of play, at stage 3 both high and low quality firms are present on the market and set two different prices (one for each quality level). If it existed, consumers would infer each firm’s quality and force low quality firms out of the market. I therefore look for equilibria with pooling introductory prices. 8Beliefs are e2 j(p1,q1,p2) = zjif q1 j>0 and I assume e2 j= 0 if q1 j= 0, to rule out the possibility that a firm finds it optimal to produce only at stage 4. The superscript 2 is due to the fact that beliefs are relevant only in the two stages of market interaction and stage 4 is the second one. 9Notice that p2(h), q2(h) and π2(h) are all decreasing functions of h. 10Strategies specify each firm’s introductory price after any possible n > 0 and z∈ {0,1}n, since this identifies any possible information set at which firms may be called to set prices. While at stage 4 any collection of previous histories of play identifies a proper subgame, this is not the case at stage 3, because, for any n, any price vector p1∈Rn +identifies one information set for the representative consumer, independently of z∈ {0,1}n. 8
or low quality products, and then repeatedly interact to sell experience goods to consumers, who are able to precisely discover a firm’s product quality only after the first purchase, but who are sufficiently rational to form correct expectations about average market quality. Although introductory prices may be used as signals of quality, consumers do not trust them if such signals are too easy to imitate. This creates a strong incentive for firms to pool on the same introductory price, independently of their quality. If high quality is sufficiently important to buyers, then all firms entering the market specialize on high quality and set initially low and rising prices. Profits from repeated purchase then more than compensate initial losses, and the reputation mechanism assures compliance with quality promises. This result has been derived under the assumption that low quality products cannot be profitably sold under perfect information. This makes separation through high prices impossible, because for low quality sellers it is always profitable to mimic such prices.20 Relaxing this assumption, equilibria in which high and decreasing prices grant high quality might emerge, as well as equilibria in which different qualities co-exist in the market and are recognized as such. Although conceptually straightforward, the analysis of such equilibria poses new technical subtleties, which require a separate work. An analogous argument applies to the assumption that the utility difference between high and low quality is much higher than the cost difference, so that low introductory prices constitute a profitable investment in reputation, independently of the degree of market competition. In a companion paper (Vanin, 2009) I show that, when high quality is not much more valuable to buyers than more costly to firms, the reputation mechanism fails and the four stage game considered here yields interesting market dynamics with equilibrium cheating. The analysis of the intermediate case, in which investing in reputation may be profitable when competition is low but not when it is high, would make derivation and presentation of results unnecessarily cumbersome, without adding much to intuition. It is to be expected that, if entry costs are low and the equilibrium number of entrants is high, then the reputation mechanism would fail, yielding equilibrium cheating by some firms; in turn, if entry costs are high and the equilibrium number of entrants is low, results would resemble those obtained here. 20This, in turn, makes consumers skeptical when they observe different market prices, unless such prices are so low that they cannot be profitably imitated by low quality firms. 15
Appendix Lemma 1. (seq. rational pooling introductory price functions) A pooling introductory price function p1(n, h, e0)is sequentially rational given beliefs (6), with e0∈ {0}∪cH−cL γ,1i, if and only if it satisfies the following conditions.21 1. ∀n > 0,∀h∈ {0, . . . , n}, p1(n, h, e0)≥cLand, if h > 0and e0= 0, then p1(n, h, e0) = cL. 2. ∀e0∈cH−cL γ,1i, p1(1,0, e0) = pE(1, e0, cL)and p1(1,1, e0) = pE(1, e0, cH). 3. ∀n > 1,∀h∈ {1, . . . , n},∀e0∈cH−cL γ,1i, p1(n, h, e0)< α(e0)and, if h > 1and p1(n, h, e0)∈(cL, α(e0)), then [p1(n, h, e0)−cH]e0γ−[p1(n, h, e0)−cL] n+ (cH−cL)1 + µ n+µγ ≥1 4−h+µ(h−1) [2h+µ(h−1)]2[γ−(cH−cL)]2.(10) Proof. Notice first that, given Assumption 1, Assumption 2 can be equivalently re-written in one of the following ways: γ≥ˆγ⇐⇒ ∀n > 0,∀h∈ {1, . . . , n}, πH(n, h, cL,1) ≥0⇐⇒ ∀n > 0, πH(n, n, cL,1) ≥0⇐⇒ limn→∞ πH(n, n, cL,1) ≥0.22 Assumptions 1 and 2, together with beliefs (6), imply that for any n > 1 and h∈ {1, . . . , n}, a high quality firm’s deviation from p1(n, h, e0)> cLto p=cLyields strictly positive overall expected profits π0 H(n, h, cL, p1(n, h, e0),1) >0. 1. If, for some n > 0 and h∈ {0, . . . , n}, p1(n, h, e0)< cL, then at the corresponding information set any firm would strictly gain by deviating to p=cL. Under beliefs (6) and Assumption 1, e0= 0 implies that demand is positive if and only if p1(n, h, 0) ≤cL. Given Assumption 2, in turn, ∀n > 0,∀h∈ {1, . . . , n}, πH(n, h, cL,1) >0. 21In the cases not explicitly considered no additional constraints are imposed. See Vanin (2007) for a generalization of this lemma outside Assumption 2. 22The precise expression of ˆγcomes from this last version. 16
2. Given Assumption 1, e0∈cH−cL γ,1iis equivalent to α(e0)> cHand therefore implies α(e0)> cL. In this case, under beliefs (6) a low quality monopolist faces exogenous quality expectations e0, whatever price it may choose in the interval (cL, α(e0)). Only if it chooses its optimal monopoly price in this interval, no profitable deviations are possible. For a high quality monopolist, an analogous argument applies. 3. When several firms initially enter the market and a pooling introductory price p1(n, h, e0)≥cLis expected, low quality ones have no profitable deviations. Any high quality firm (h > 0) may guarantee itself zero overall expected profits through a deviation to p>cL; if it deviates from p1(n, h, e0)> cLto p≤cL, it monopolizes the market at both stages 3 and 4, but it makes initial losses (so that the best such deviation is to p=cL). Assumptions 1 and 2, together with beliefs (6), imply that, given e0>0, a pooling introductory price p1(n, h, e0)≥α(e0) is not sequentially rational, because it yields zero overall expected profits and high quality firms would gain by deviating to p=cL. A pooling price p1(n, h, e0)∈(cL, α(e0)), in turn, is sequentially rational if and only if πH(n, h, p1(n, h, e0), e0)≥0 and πH(n, h, p1(n, h, e0), e0)≥π0 H(n, h, cL, p1(n, h, e0),1). The former inequality holds for any n > 1 and h > 0, because e0>0 and p1∈ (cL, α(e0)) imply that πH(n, h, p1, e0)> πH(n, h, cL,1) ≥0. If h= 1, the second inequality also holds for any n > 1 and e0>0, because by deviating from p1∈(cL, α(e0)) to p=cL, the high quality firm would simply worsen its initial losses (or start to make them) without any future benefit. In turn, if h > 1, then initial deviation losses might pay off in the future (in terms of reduced competition), so that sequential rationality requires πH(n, h, p1(n, h, e0), e0)≥π0 H(n, h, cL, p1(n, h, e0),1), which is is equivalent to condition (10). References Allen, F. (1984). Reputation and product quality. RAND Journal of Economics 15(3), 311–327. 17
Bagwell, K. and M. H. Riordan (1991). High and declining prices signal product quality. The American Economic Review 81(1), 224–239. Bester, H. (1998). Quality uncertainty mitigates product differentiation. RAND Journal of Economics 29(4), 828–844. Cooper, R. and T. W. Ross (1984). Prices, product qualities and asymmetric information: The competitive case. Review of Economic Studies 51(2), 197–207. Daughety, A. F. and J. F. Reinganum (2007). Competition and confidentiality: Signaling quality in a duopoly when there is universal private information. Games and Economic Behavior 58(1), 94–120. Daughety, A. F. and J. F. Reinganum (2008). Imperfect competition and quality signalling. RAND Journal of Economics 39(1), 163–183. Fluet, C. and P. G. Garella (2002). Advertising and prices as signals of quality in a regime of price rivalry. International Journal of Industrial Organization 20, 907–930. Hertzendorf, M. N. and P. B. Overgaard (2001). Price competition and advertising signals: Signaling by competing senders. Journal of Economics & Management Strategy 10(4), 621–662. H¨orner, J. (2002). Reputation and competition. American Economic Review 92(3), 644–663. Klein, B. and K. B. Leffler (1981). The role of market forces in assuring contractual performance. The Journal of Political Economy 89(4), 615– 641. Milgrom, P. and J. Roberts (1986). Price and advertising signals of product quality. The Journal of Political Economy 94(4), 796–821. Motta, M. (2004). Competition Policy. Theory and Practice. Cambridge, UK: Cambridge University Press. Overgaard, P. B. (1994). Equilibrium effects of potential entry when prices signal quality. European Economic Review 38(2), 367–383. 18
Shapiro, C. (1983). Premiums for high quality products as returns to reputation. The Quarterly Journal of Economics 98(4), 659–680. Shubik, M. and R. Levitan (1980). Market Structure and Behavior. Cambridge, MA: Harvard University Press. Toth, A. (2008). The great industry gamble: Market structure dynamics with moral hazard. Mimeo, University of Warwick. Vanin, P. (2007). Industrial Organization, Trade and Social Capital. Ph. D. thesis, Universitat Pompeu Fabra, Barcelona, Spain. Vanin, P. (2009). Competition, reputation and cheating. Mimeo, Universit`a di Bologna. Yehezkel, Y. (2008). Signaling quality in an oligopoly when some consumers are informed. Journal of Economics & Management Strategy 17(4), 937– 972. 19