Learning Quality from Prices and Word-of-Mouth Communication

Transcription

1 Learning Quality from Prices and Word-of-Mouth Communication Carla Guadalupi May 10, 2016 Abstract This paper studies the eect of word-of-mouth communication on the optimal pricing strategy for new experience goods. I consider a dynamic monopoly model with asymmetric information about product quality, in which consumers learn in equilibrium from both prices and other consumers. The price provides a signal from which consumers can infer the rm's type and therefore product quality, even as it inuences the rate of information transmission via interpersonal communication. The main result is that word-of-mouth communication guarantees the existence of separating equilibria, wherein the highquality monopolist signals high quality through a low introductory price, and the low-quality monopolist charges a higher introductory price. The intuition is simple: low prices are costly, and will only be used by rms condent enough that increased experimentation and therefore communication among consumers will yield good news and therefore increased future prots. Moreover, for the high-quality seller, the expected price quantity dynamic is increasing decreasing over time; whereas for the low quality one the opposite is true. Finally, signaling becomes more dicult when consumers pay less attention to their peers' reports and more attention to past prices. KEYWORDS: Price signaling, word-of-mouth communication, monopoly, learning. JEL CODES: L12, L15, D21, D42, M31. Departamento de Economía de la Empresa, Universidad de las Islas Baleares, Ctra. Valldemossa km. 7.5, Palma de Mallorca, España, carla.guadalupi@uib.es I would like to express special thanks to Luis Cabral, Gonzalo Cisternas, Juan Pablo Montero, and Carlos Ponce for helpful comments and constructive criticism; participants at the Sao Paolo University Game Theory Workshop and the Universidad de Chile Industrial Organization Workshop, and especially Nicolás Figueroa, Gastòn Llanes and Joaquín Poblete for discussions and brilliant suggestions. Special thanks are given to Conicyt for the nancial support in the form of Doctoral Scholarship. 1

2 1 Introduction Word-of-mouth communication is a powerful instrument to disseminate product information before purchase. When consumers face uncertainty about the characteristics and quality of a newly-introduced product, they are able to learn from their peers and tend to pay attention to what their fellow consumers observed in past purchases through experimentation and word-of-mouth Arndt 1967; Chen and Xie 2008; Zhu and Zhang Furthermore, advances in information technology have conrmed that consumers exchange a great deal of information on products via social networking sites and other online fora Bickart and Schindler, 2001; Godes and Mayzlin, 2004; Chevalier and Mayzlin, In general, word-of-mouth communication is pervasive in markets for experience goods, whose quality is unobserved at the time of purchasing, and only becomes known after consuming and tasting the product. In the case of new experience goods, the rm often has a precise idea of the quality of the product it provides. When the seller is better informed about the characteristics and quality of the product, also prices may provide valuable information to consumers, as they can be used by the rm as signals of quality. Extensive literature has explored the optimal pricing strategy and dynamics for new products of initially uncertain quality to consumers. Nevertheless, most signaling models have ignored learning from others and the question of whether and how interpersonal communication across consumers aects or is aected by prices. It is, therefore, interesting to study how a high-quality seller can take strategic advantage of experimentation and word-of-mouth, when choosing his pricing strategy. This paper addresses these questions by providing a simple model in which word-of-mouth communication is combined with strategic pricing and signaling. I use a dynamic model with asymmetric information regarding quality and word-of-mouth communication, to characterize the monopolist's optimal pricing strategy for introducing a new product. The model and results are based on the following ideas. The price provides a signal from which buyers can infer the rm's type and therefore the quality of the product, even as it inuences the rate of information transmission among consumers via interpersonal communication. More sales lead to higher product exposure in the subsequent period, which amplies the good or bad news generated by the product through word-ofmouth communication, so that prices become an instrument through which the rm may signal quality by encouraging or discouraging experimentation and controlling the diusion of information. Specically, I consider a two-period model, in which a long-lived monopolist introduces a new experience good of unknown quality to consumers. The monopolist can be either a high or low-quality seller, which is private information. Consumers are short-lived and the satisfaction they receive from buying the product is a function of both the objective quality and a personal taste or preference. First-period consumers can only rely on prices to infer the monopolist's type therefore product quality, and make a purchase decision. Only 2

3 after purchase and consumption they are able to observe quality. For second-period consumers, on the other hand, learning comes from the observation of noisy signals of past prices and word-of-mouth communication with past consumers. The reason why past prices are not always observable is that public information about prices usually reects posted prices, without taking into account discounting, clearance sales or local retail variations, which can have little resemblance to actual transaction prices 1. Moreover, consumers often do not remember the actual price they paid for the product. Second, I allow second-period consumers to communicate with some neighbors past consumers, who report the satisfaction obtained from the product, if purchased. Reports from past consumers are noisy signals of the observed quality, since higher satisfaction can come either from high quality or from high personal preference. Moreover assuming that only a fraction of past consumers communicate with new ones seems realistic since social interaction is unlikely to reveal what the whole world is doing, but just a small portion of it. Nevertheless, information gathered through word-of-mouth communication is more precise when the fraction of neighbors who bought in the past is high, which in turn implies that more sales in the rst period guarantee more precise learning in the second period 2. I analyze the role of prices as signals of quality when consumers learn in equilibrium from both prices and word-of-mouth communication. In other words, I dene and study conditions for the existence of separating equilibria. First, I characterize the benchmark case, and show that there is no separating equilibrium without word-of-mouth communication among consumers. I then show that, when allowing for word-of-mouth communication, a separating equilibrium does exist in which prices signal quality. I nally provide an example of information structure and study how the separating equilibrium responds to variation in the signals' precision. The main result is that word-of-mouth communication among consumers is essential for the existence of a separating equilibrium. Moreover, in any separating equilibrium, the high-quality monopolist signals high quality through a low introductory price, whereas the low-quality monopolist charges a higher introductory price. The inuition behind this result is simple: low prices are costly, and will only be used by rms condent enough that increased experimentation and therefore communication among consumers will yield good news and therefore increased future prots. The high-quality monopolist aims to maximize the benets from consumer communication through increased sales, and therefore uses a low price as a signal of quality. The low-quality monopolist, on the other hand, avoids information transmission by choosing a higher price, which limits sales and the probability that future consumers learn through word-of-mouth. Some additional implications: for the high-quality seller, the expected price quantity dynamic is increasing decreasing over time; whereas for the low quality one the opposite is true. Since the second-period price is a function of beliefs, 1 See Caminal and Vives 1996 for a more detailed explanation of no observable price history. 2 See Banerjee and Fudenberg 2004 for a more detailed explanation of why consumers are often allowed to communicate with just a fraction of previous ones. 3

4 it will be higher lower if good bad news is revealed in the rst period when the product was introduced. Moreover, the low separating price charged by the high-quality monopolist in equilibrium decreases as the impact of signaling on consumers' beliefs increases: a high-quality seller must work harder to discourage the low-quality one from mimicking its behavior if consumers pay less attention to their peers' reports. Finally the only separating equilibrium that satises the intuitive criterion is such that the low-quality monopolist charges his prot-maximizing price, whereas the high-quality one charges the highest of the low prices that the low-quality monopolist will not nd protable to mimic. Related Literature. This paper is closely related to the literature on signaling quality through prices. Milgrom and Roberts 1986 analyze a dynamic signaling model in which both the introductory price and level of advertising can signal quality. Their focus is on separating equilibria involving advertising as the main tool to signal high quality, and their argument is based on repeat purchases. Bagwell and Riordan 1991 show that high and declining prices signal high quality, in a static model for durable goods and for dierent informational settings. This result is due to cost eects: signaling through high prices generates lower sales, which are less damaging to a higher-cost producer. Linnemer 2002 extends their work including advertising as a choice variable for the rm, obtaining the same result that both high prices and dissipative advertising are interpreted as signals of high quality by uninformed consumers. Judd and Riordan 1994 reach the same result by examining a two-period signal-extraction model with learning. Even though no correlation between quality and costs is assumed, private information on both sides of the market allows the seller to signal high quality through high prices. I depart from these models in that I take into account experimentation and learning from others, and how the interaction between consumers aects the rm's pricing strategy. In particular the standard result in the signaling literature you get what you pay for is reverted when allowing for word-of-mouth communication among subsequent generations of consumers. This paper is also related to the literature on strategic experimentation, where both the rms and consumers are initially uncertain about the product quality. Since high levels of initial sales help both sides of the market obtain information, low prices are optimal Bergemann and Valimaki 1996, 1997; Caminal and Vives, 1999; Schlee, No information asymmetries are considered in the experimentation literature, therefore no signaling arises. Signaling quality through quantities is the main scope of Caminal and Vives 1996 and Vettas Caminal and Vives 1996 consider a duopoly model in which consumers face uncertainty about the quality dierentials of the competing products and study the informational role of quantities. By cutting prices the rms can attempt to make consumers think the product sells more because of its higher quality and not simply because it is cheap. Their main focus is on market shares as the main tool to signal quality, even though there is no communication among consumers. The paper closest to this is Vettas 1997, who studies the informational role of quantities when allowing for word-of-mouth communication among 4

5 consumers. A monopolist introduces a durable good of initially uncertain quality to consumers that learn from previous users who have experienced the product. The monopolist controls the amount and speed of information diusion through the strategic choice of quantities. In this model, there is no separating equilibrium in which prices signal quality, but only a pooling one, in which a high-quality seller spreads sales to incentivize communication between consumers, and therefore information transmission. I extend the last model by allowing learning in equilibrium from both prices and other consumers. In particular I nested word-of-mouth learning, as modeled in Banerjee and Fudenberg 2004, in a two-period signaling model, in which learning in equilibrium comes from both prices and other consumers. Moreover I exploit the fact that learning is noisy in the second period and the signals consumers receive can be ordered according to the precision criteria established by Ganuza and Penalva 2010, which facilitates the existence proof. 2 The Model I consider a two-period model, in which a long-lived monopolist introduces a new experience good of unknown quality to consumers. Quality q is a random variable distributed according to F θ q, with positive and dierentiable density f θ q. The parameter θ {H, L} represents the monopolist's type, which is private information and can be high or low. The distributions F θ q are ordered by rst-order stochastic dominance FOSD, with F H q < F L q 3. Quality is exogenous and can be thought of as determined by R&D prior to production, therefore unrelated to marginal costs, which I assume are zero for both types. Consumers are short-lived and represented by a continuum of mass 1. They have unit demand for the product and receive satisfaction r i q, v i if they purchase and zero otherwise. The satisfaction r i q, v i is an increasing function of the common valuation objective quality q and the individual valuation taste v i, an independent draw from distribution G v i with positive and dierentiable density g v i. Therefore consumers' satisfaction provides valuable, but noisy, information about the objective quality q of a product. The timing of the game is as follows: the monopolist learns his type and chooses an introductory price. After observing the price, consumers update beliefs on the monopolist's type and therefore product quality and make their purchase decisions. Quality is then observed. At the beginning of the second period, new consumers enter the market and form their beliefs by observing noisy signals of past price and observed quality. The monopolist then sets the second-period price. Given second-period beliefs and price, consumers make a purchase decision. Second-period prots are realized and the game ends. Consumers' beliefs and information structure. Consumers share the prior belief µ 0 that the monopolist is a high-quality producer. First-period consumers can only rely on prices to update beliefs. Separating 3 I assume permanent types, therefore quality realizations q are independent draws from the same distribution F θ q in both periods. Moreover quality is the same for all units produced in each period. 5

6 prices P L, P H induce beliefs µ = 0 if P = P L and µ = 1 if P = P H 4. Moreover I restrict o-the-equilibrium path beliefs such that any deviation is attributed to the low-quality seller. Consumers learn their personal valuation v i and decide whether to buy given P ; µ and v i. They buy if and only if E µ [r i q, v i P ] 0, which leads to the aggregate rst-period demand D P, µ. Second-period consumers have two mechanisms to infer the monopolist's type: noisy signals of past price and observed quality. Specically, they observe a noisy signal of P, from which infer the belief µ µ about the monopolist's type price signal, as a function of the true µ. Additionally, they communicate with randomly sampled rst-period consumers, who report the satisfaction obtained from the product, if purchased. Note that the number of reports received is proportional to the aggregate rst-period demand D P, µ. Therefore, for a realized objective quality q and an average report r i q, v i 5, second-period consumers infer the belief λ q, r i quality signal about the monopolist's type: λ q, r i = P θ = H q, r i. The expected value of which, given q, is Λ q = E θ = H q, r i. After observing both the price and quality signals, consumers form second-period beliefs µ 2, as a function of µ, λ q, r i, and D P, µ. From the previous analysis, µ 2 can be written as µ 2 µ, Λ q, D P, µ 6. The relative inuence of each signal depends on its respective informative content and precision. The signal ordering relies on the notion of supermodular precision as dened by Ganuza and Penalva 2010, which allows signals to be ordered in terms of their relative impacts on the distribution of conditional expectations 7. The quality signal Λ q is more supermodular precise if the past quantity sold D P, µ is higher, since it increases the number of useful reports. Moreover, more precise informative signals will have higher inuence on updating consumers' beliefs see Lemma 1 in Ganuza and Penalva Therefore second-period beliefs satisfy the following conditions: 1. 2 µ 2µ,Λq,DP,µ DP,µ Λq > µ 2µ,Λq,DP,µ µ Λq > 0 4 In other words, by observing the separating price, consumers will authomatically know from which distribution quality has been drawn. On the other hand, pooling prices do not provide any information and the posterior is unaltered, µ = µ 0. 5 For simplicity, I drop the problem of integrality of the number of reports. 6 From now on, for simplicity, I call µ and Λ q the price and quality signal, respectively. 7 Basically, an information structure the joint distribution of the unknown parameter and the signal is more informative more precise than another if it generates a more disperse distribution of conditional expectations. 6

7 which ensure that an increase in the quantity sold in the rst period directly or through higher rstperiod beliefs makes word-of-mouth communication more informative. After observing their individual taste v i, second-period consumers decide whether to buy given P 2, µ 2 and v i. They buy if and only if E µ2 [r i q, v i P 2 ] 0, which leads to the aggregate second-period demand D P 2, µ 2. Prots. Let Π θ, P, µ denote the expected prots of a monopolist of type θ who charged the price P in the rst period, inducing beliefs µ: ˆ Π θ, P, µ = P D P, µ + π µ 2 µ, Λ q, D P, µ f θ q dq, q where π µ 2 represents second-period prots, which are increasing and convex in beliefs, and satisfy the following assumption: Assumption 1. Second-period marginal prots are increasing in observed quality: 2 π µ 2 µ, Λ q, D P, µ P q > 0. Assumption 1 ensures that an increase in rst-period demand is more benecial to the high-quality monopolist. In particular µ 2 is an increasing function of D P, µ for high quality realizations, whereas it is decreasing in D P, µ for low quality realizations. An increase in D P, µ will be detrimental to beliefs when news is bad and quality poor, whereas it will improve the monopolist's reputation and prots when news is good. Note that this eect is more pronounced for the low-quality seller which has a worse in the sense of FOSD quality distribution. I dene and analyze conditions for the existence of separating equilibria in pure strategies. First I characterize the benchmark case, and show that there is no separating equilibrium without word-of-mouth communication. I then show that, when allowing for word-of-mouth communication, a separating equilibrium does exist in which prices signal quality. I nally provide an example of information structure and study how the separating equilibrium responds to variation in the signals' precisions. 3 Separating Equilibrium This paper considers the role of prices as signals of quality when consumers learn in equilibrium through 7

8 word-of-mouth communication. Therefore it is natural to focus on separating equilibria. In this context, separating equilibria are prefect Bayesian equilibria at which consumers can distinguish between the high and low-quality producer by their dierent pricing choices. Even though the main objective is the dynamic setting, note that signaling occurs only in the rst stage of the game. The assumption that types are permanent prevents the need to consider repeated signalling. In a separating equilibrium, consumers know once and for all the monopolists type once the introductory price is chosen. A separating equilibrium P L, P H induces beliefs µ = 0 if P = P L and µ = 1 if P = P H. Moreover, o-equilibrium prices P P L, P H are assumed to induce pessimistic beliefs µ = 0. Denition 2. A rst-period separating equilibrium is a pair P L, P H such that: C1. Π L, P L, µ = 0 Π L, P, µ = 0, for every P P H. C2. Π L, P L, µ = 0 Π L, P H, µ = 1, and C3. Π H, P H, µ = 1 Π H, P, µ = 0, for every P P H. For the low-quality monopolist, the equilibrium price P L must dominate any price P P H that induces the same pessimistic beliefs C1. Moreover, the low-quality monopolist should not have incentives to mimic its high-quality counterpart, even if this implies optimistic beliefs C2. For the high-quality monopolist, P H must dominate any other price P, knowing that any deviation will be treated as coming from a low-quality seller C3. Lemma 3 follows from Denition 2. Lemma 3. In any separating equilibrium P L = P L, where P L is the price the maximizes the lowquality monopolist's expected prots monopoly price. For the high-quality one, it is sucient to check that Π H, P H, µ = 1 Π H, P H, µ = 0, where P H is the high-quality monopoly price. Proof. A necessary condition for C1 to be satised is that the low-quality monopolist charges in equilibrium the monopoly price P L in equilibrium. That is the price that maximizes expected prots under the correct beliefs µ = 0. Moreover C3 requires that the high-quality monopolist should not have any incentive to deviate from the equilibrium price, as such deviation implies pessimistic beliefs. Then it is sucient to control for the best deviation, which occurs at monopoly price, P H, the maximizer of Π H, P, µ = 0. 8

9 3.1 Benchmark case: prices without word-of-mouth communication Although the main problem considered here allows for word-of-mouth communication among consumers, it is useful to establish a benchmark case in order to compare its eects on the existence and characterization of separating equilibria. The static problem here is the following 8. The monopolist introduces a new experience good of unknown quality to consumers. The monopolist is aware of his type - the distribution function from which quality is drawn - and chooses price strategically. Consumers observe the price and update beliefs accordingly. They learn their individual valuation for the product, and given prices and beliefs, make a purchase decision. Then quality is observed. The rst result is that, when no communication among consumers is permitted, there is no fully revealing equilibrium in which prices signal quality. The only existing equilibria are pooling. Moreover, the only pooling equilibrium that survives the undefeated criterium proposed by Mailath et al 1993, is one in which the monopolist chooses its preferred price, that is the price that maximizes prots under the prior belief µ 0. Lemma 4. There is no separating equilibrium without word-of-mouth communication. Indeed, the only pooling equilibrium that survives the undefeated renement is P, the maximizer of P D P, µ 0. If consumers are not allowed to communicate about the observed quality, any price chosen by the highquality seller can be costlessly mimicked by the low-quality counterpart. This is because the high-quality monopolist cannot protably use the price to manipulate information revelation and transmission among second-period consumers. Therefore any equilibrium will be a pooling one. Nevertheless, the restriction on o-equilibrium beliefs makes most pooling equilibria implausible. The only pooling equilibrium that satises the undefeated criterium is the one in which the high-quality seller chooses his preferred price and the low-quality one mimics him. 3.2 Prices with word-of-mouth communication I now consider the two-period model, in which consumers can learn through prices and word-ofmouth communication, and solve the game using backward induction. Following any history of separation P L, P H, second-period prices maximize P 2 D P 2, µ 2 µ, Λ q, D P, µ, which leads to second-period protsπ µ 2 µ, Λ q, D P, µ. I look for rst-period separating equilibria as dened in Denition 2, and 8 For simplicity I consider the static version of the game, in which consumers learn from prices and are not allowed to communicate with their peers. The same result holds for the two-period extension, without word-of-mouth communication. 9

10 apply the intuitive criterion renement Cho and Kreps, 1987 to eliminate implausible o-equilibrium beliefs. The main result is that word-of-mouth communication allows the existence of separating equilibria, in which the high-quality monopolist signals high quality through a low introductory price lower than the monopoly price, whereas the low-quality monopolist charges a higher introductory price the monopoly price. Proposition 5. With word-of-mouth communication, there is always a separating equilibrium P L, P H with P H < P H. The inuition behind this result is simple: low prices are costly, and will only be used by rms condent enough that increased experimentation and therefore communication among consumers will yield good news and therefore increased future prots. The high-quality monopolist aims to maximize the benets from consumer communication through increased sales, and therefore uses a low price as a signal of quality. The low-quality monopolist, on the other hand, tries to avoid information transmission by choosing a higher price, which limits sales and the probability that future consumers learn through word-of-mouth. This result contraddicts the standard literature of signaling quality thorugh prices, according to which high prices signal high quality. Moreover it complements the literature of quantity as signals of quality by characterizing the optimal pricing strategy and path when word-of-mouth communication among consumers is permitted. As shown in Figure 1, the existence of a separating equilibrium is implied by three conditions: i P H < P L, ii 2 Πθ,P,µ θ P < 0 standard single-crossing, and iii 2 Πθ,P,µ θ µ > 0 sensitivity single-crossing. Condition i states that the monopoly price, the price that maximizes expected prots, is higher for the low-quality seller than for his high-quality counterpart. The intuition behind this result is the following. Even when allowed to choose the optimal price, the high-quality monopolist will prefer to set a lower price than his low-quality counterpart, holding beliefs constant. This result is implied by the standard single-crossing property ii: the cost of signaling through low prices is lower for the high-quality monopolist. The third condition iii requires that the shift from pessimistic to optimistic beliefs is more attractive to the high type than to his low-type counterpart 9. It follows, from Proposition 5, that there is no separating equilibrium in which high prices signal high quality. This is because any price higher than the monopoly price P H is attractive to, and therefore 9 In Spence's job-market signaling model, good-type workers signal high-quality via increased education, which at some critical point bad types are unable to replicate because education is assumed to be more costly for them. Here, the logic of the signaling mechanism does not depend on cost dierences across types, instead copycat behavior is prevented by repeat purchases due to the existence of a second-period with improved information standard-single crossing. Nevertheless, in contrast to Spence s model where the worker s utility, quasilinear in beliefs, ensures condition iii, in our setup, signaling also requires prots to be marginally more sensitive to type for beliefs µ sensitivity single-crossing. 10

11 Figure 1: Sketch of the Proof represents a protable deviation for, a low-quality seller. The result is due to the properties of second-period beliefs, which guarantee that standard single-crossing is negative. As more supermodular precise signals have higher inuence on updating consumers' beliefs, an increase in the quantity sold in the past D P, µ, ensures a higher impact of the quality signal Λ q on second-period beliefs µ 2, which in turn makes the existence of separating equilibria in which high prices low quantities 10 signal high quality impossible. Some additional implications: for the high-quality seller, the expected price quantity dynamic is increasing decreasing over time; whereas for the low-quality one the opposite is true. Since the second-period price is a function of beliefs, it will be higher lower if good bad news is revealed in the rst period when the product was introduced. Most of these separating equilibria involve beliefs that are implausible, since any deviation is interpreted as coming from a low-quality seller. To solve the problem of multiplicity of equilibria that arises in standard signaling games, I restrict attention to those equilibria that satisfy the intuitive criterion proposed by Cho and Kreps To understand the renement in this context, consider an equilibrium in which the high-quality monopolist's prots are Π H, P H, µ = 1 while the low-quality monopolist earns prots Π L, P L, µ = 0. This equilibrium fails the intuitive criterion if there exists a price P ' such that: a Π H, P, µ = 1 Π H, P H, µ = 1 and b Π L, P, µ = 1 < Π L, P L, µ = 0. That is, if there exists a price P such that the high type is better o by deviating and the low type makes more prots following the equilibrium strategy, even if the deviation would have generated optimistic beliefs. Intuitively, if such a price P exists, consumers should interpret such a deviation as coming from a high-quality seller, collapsing the equilibrium. The only 10 Note that in the experimentation process, second-period consumers observe some noisy signal of the past quantity for instance the number of people they meet who tell them they have purchased the product and how satised they were. Hence signaling through low prices or high quantities will yield the same result. 11

12 pair that survives the intuitive criterion is P L, P. As in any separating equilibrium, the low-quality monopolist charges his monopoly price, whereas the high-quality one charges the highest of the low prices that the low-quality monopolist would not nd protable to mimic. Proposition 6. The pair P L, P is the only separating equilibrium that satises the intuitive criterion. 3.3 Truth or Noise Application I now provide an example of an information structure that can be ranked according to the supermodular precision proposed by Ganuza and Penalva 2010, and show that, under this information structure, secondperiod beliefs indeed satisfy the conditions 2 µ 2µ,Λq,DP,µ DP,µ Λq > 0 and 2 µ 2µ,Λq,DP,µ µ Λq > 0, as required for the existence proof Proposition 4. Given this information structure, I then show how the separating equilibrium reacts to changes in the signals' precisions. When second-period consumers enter the market, they have two mechanisms to infer the monopolist's type: noisy signals of past price and observed quality. More precisely, the observation of a noisy signal of P induce an imperfect belief µ µ about the monopolist's type, the price signal. Similarly, communication with K past consumers about the satifaction obtained from purchaising the product, r i q, v i, induce an imperfect belief λ q, r i about the monopolist's type, the quality signal. Moreover the number of reports received is proportional to the quantity sold by the monopolist in the rst period, that is K D P, µ with K increasing in D P, µ. Note that both the price and quality signal are functions of the true underlying beliefs, µ and Λ q, respectively 11. Therefore µ 2, the conditional expectation on the monopolist's type after receiving the two signals, is dened as function of µ, Λ q and D P, µ. The information structure I consider here is the truth or noise technology, as rst dened by Lewis and Sappington 1994, or linear experiment, as dened by Ganuza and Penalva A truth or noise signal returns the true parameter with some probability, and pure noise with the complementary probability. Let the monopolist's type θ Θ be distributed according to a function F θ with mean µ 0, and let µ and λ be two signals about the true parameter θ. With probability k, µ = µ, and with probability 1 k, µ = ε, with ε = µ 0. Similarly, with probability K D P, µ, λ q, r i = Λ q, and with probability 1 K D P, µ, no reports are received, therefore λ q, r i = ε, with ε = µ 0. Then µ 2 µ, Λ q, D P, µ := E θ = H µ, λ 11 The price and quality signals provide imperfect information about the beliefs µ = Pθ = H P and Λ q = P θ = H q, respectively. 12

13 = kµ + 1 k K D P, µ Λ q + 1 k 1 K D P, µ µ 0. The relative impact of each signal on second-period beliefs depends on its respective informative content and precision. The signal ordering relies on the notion of supermodular precision as dened by Ganuza and Penalva 2010, which allows to order signals in terms of their relative impact on the distribution of conditional expectations 12. Note that the quality signal λ is more supermodular precise if quantity sold in the past D P, µ is higher, since it increases the amount of reports received see Proposition 4 in Ganuza and Penalva Moreover, the more supermodular precise signal has a conditional expectation function that is more sensitive to changes in the realization of the signal. In other words, when the quantity sold in the rst period is higher, the quality signal will have a higher impact on beliefs µ 2 see Lemma 1 in Ganuza and Penalva Therefore second-period beliefs show the following properties: and 2 µ 2µ,Λq,DP,µ µ Λq 2 µ 2µ,Λq,DP,µ DP,µ Λq > 0 > 0, which ensure that an increase in the quantity sold in the rst period directly or through higher rst-period beliefs makes the quality signal Λ q more supermodular precise, and therefore increases its impact on beliefs µ 2 µ, Λ q, D P, µ. In particular: 2 µ 2 µ, Λ q, D P, µ D P, µ Λ q = K D P, µ D P, µ 1 k > 0 2 µ 2 µ, Λ q, D P, µ µ Λ q = K D P, µ D P, µ 1 k > 0. D P, µ µ 3.4 Comparative static on the equilibrium price P In section 3.2 I applied the intuitive criterion to select among equilibria in order to rule out counterintuitive equilibria driven by pessimistic beliefs, and showed that the only pair that survives the intuitive criterion is P L, P. As in any separating equilibrium, the low-quality monopolist charges his monopoly price, whereas the high-quality one charges the highest of the low prices that the low-quality monopolist would not nd protable to mimic. Consider now the information structure truth or noise described in section 3.3, which leads to second-period beliefs: µ 2 µ, Λ q, D P, µ = kµ + 1 k K D P, µ Λ q + 1 k 1 K D P, µ µ Basically, an information structure the joint distribution of the unkown parameter and the signal is more informative more precise than another if it generates a more disperse distribution of conditional expectations. 13

14 It is interesting to analyze how the price P reacts to an increase in k, that is how the equilibrium changes when signaling through the belief µ has a higher impact on second-period beliefs. The main result is that a higher impact of rst-period prices on second-period beliefs decreases the separating price charged by the high-quality seller in t = 1. A good signal in the rst period P = P H carries more positive information to second-period buyers, making it more attractive. To discourage the low-quality seller from mimicking, a lower price must be charged by the high-quality monopolist. Proposition 7. The separating equilibrium price P is decreasing in k. 4 Conclusion This paper studies the optimal pricing strategy for new experience goods in a dynamic monopoly model with private information about product quality and word-of-mouth communication among consumers. While rst-period consumers can only rely on prices to infer the monopolist's type therefore product quality, for second-period consumers learning is noisy. In particular, second-period consumers infer the monopolist's type from noisy signals of the past price and the observed quality. The main result is word-of-mouth communication allows signaling through low prices. In particular, in any separating equilibrium the high-quality monopolist signals high quality through a low introductory price lower than the monopoly price, whereas the low-quality monopolist charges a higher introductory price the monopoly price. The intuition behind this result is simple: low prices are costly, and will only be used by rms condent enough that increased experimentation and therefore communication among consumers will yield good news and therefore increased future prots. The high-quality monopolist aims to maximize the benets from consumer communication through increased sales, and therefore uses a low price as a signal of quality. The low-quality monopolist, on the other hand, avoids information transmission by choosing a higher price, which limits sales and the probability that future consumers learn through word-of-mouth. Some additional implications: for the high-quality seller, the expected price quantity dynamic is increasing decreasing over time; whereas for the low quality one the opposite is true. The main contribution of this paper is to allow learning in equilibrium from both prices and other consumers, through word-of-mouth communication. In particular I nested word-of-mouth learning, as modeled in Banerjee and Fudenberg 2004, in a two-period signaling model. Moreover I use the precision criteria proposed by Ganuza and Penalva 2010 to order signals that consumers receive in the second-period. This innovative approach allows to rank signals based on their relative precision and impact on the beliefs' function, and show that the higher the quantity sold in the rst period the higher the weight consumers will 14

15 assign to word-of-mouth communication, which in turn garantees the existence of a separating equilibrium in which low prices signal high quality. Many interesting extensions can be derived from this two-period framework. For example, the rm can separate and communicate quality through other instruments, such as future discounts for repeat consumers, return policies or advertising. Adding these instruments can test the model's robustness. Advertising, for example, can reveal the importance of the price instrument when word-of-mouth is the main learning force. As signaling becomes more important in belief formation, the importance of advertising as a signaling tool should increase. On the other hand, when experimentation and word of mouth are the only learning mechanism, the use of low introductory price does more to improve future sales than advertising. Another interesting extension will be studying the impact of networks and focal consumers on word-of-mouth communication and signaling quality. Finally it will be interesting to study the impact of duopolistic competition among rms on the equilibrium price and optimal signaling strategy. 15

16 Appendix Proof of Lemma 4. Let π P, µ = P D P, µ denote the one-period prots of a monopolist of type θ who sets the price P, inducing beliefs µ. Note that the prot function is independent on the monopolist's type. Intuitively there is no space for the high-quality monopolist to choose an action that his low-quality counterpart will not mimic, given the optmistic beliefs generated in equilibrium and the absence of communication among consumers about the observed quality. We prove this result by contradiction. Adapting Denition 2 and Lemma 3, the pair P L, P H is a separating equilibrium if two conditions hold: C1 π P L, µ = 0 π P H, µ = 1, and C2 π P H, µ = 1 π P H, µ = 0. Consider a separating equilibrium P L, P H where P H = P such that π P L, µ = 0 = π P, µ = 1. At this price the high-quality seller should not have any incentive to deviate to his monopoly price, π P, µ = 1 > π P H, µ = 0, or equivalently π P L, µ = 1 > π P H, µ = 0. This cannot be true since the monopoly price under pessimistic beliefs, µ = 0, is independent on the monopolist's type, then P H = P L. The only existing equilibrium of this game is a pooling one. Note that all the prices such that π P, µ = µ 0 π P θ, µ = 0 are pooling equilibria. Nevertheless most of them are supported by implausible o-equilibrium path beliefs, since every deviation is tought of as coming from a low-quality seller. Such implausible equilibria can be ruled out by the undefeated renement proposed by Mailath et. al In particular the only pooling equilibrium that survives the undefeated renement is P, the price that maximizes π P, µ 0 = P D P, µ 0. Consider a proposed equilibrium P < P and the price P, chosen in an alternative equilibrium by some rm's type. If some type prefers the alternative equilibrium price P to the proposed one and this preference is strict for at least one type, then consumers' beliefs that the deviator is of that type are increasing. Then a protable deviation appears for the rm that upset the equilibrium. Note that here both types would strictly prefer to deviate to the alternative equilibrium price, therefore the only undefeated equilibrium involves rms pooling at P. Proof of Proposition 5. As a corollary of Lemma 3, two conditions garantee the existence of a separating equilibrium: C1 Π L, P L, µ = 0 Π L, P H, µ = 1, and C2 Π H, P H, µ = 1 Π H, P H, µ = 0. 16

17 Consider the price P < P H, such that the low-quality monopolist is indierent between following the equilibrium strategy or mimic his high-quality counterpart, Π L, P, µ = 1 = Π L, P L, µ = 0. At this price the high-quality monopolist should not have any incentive to deviate to his monopoly price: Π H, P, µ = 1 Π H, P H, µ = 0 > Π L, P, µ = 1 Π L, P L, µ = 0 = 0, which is equivalent to [ Π H, P, µ = 1 Π H, P, µ = 0 ] + [ Π H, P, µ = 0 Π H, P H, µ = 0 ] > [ Π L, P, µ = 1 Π L, P, µ = 0 ] + [ Π L, P, µ = 0 Π L, P L, µ = 0 ]. Therefore it is enough to show that 1. [ Π H, P, µ = 0 Π H, P H, µ = 0 ] > [ Π L, P, µ = 0 Π L, P L, µ = 0 ] 2. [ Π H, P, µ = 1 Π H, P, µ = 0 ] > [ Π L, P, µ = 0 Π L, P L, µ = 0 ], as illustrated in Figure 1. Figure 2: Sketch of the Proof Condition 1 is implied by P H < P L and 2 Πθ,P,µ θ P < 0: 2 Π θ, P, µ θ P = { ˆ } P D P, µ + π µ 2 µ, Λ q, D P, µ f θ q dq θ P q 17

18 = D P, µ P Note that DP,µ P {ˆ q = {ˆ P q π µ 2 µ, Λ q, D P, µ f } θ q θ dq π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ } µ 2 µ, Λ q, D P, µ fθ q D P, µ θ dq < 0 and it is independent of q. Therefore it is enough to show that q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ because of FOSD of f with respect to θ. = Λ q q q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ 2 π µ 2 µ, Λ q, D P, µ 2 µ 2 µ, Λ q, D P, µ Λ q + q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ > 0 D P, µ µ 2 µ, Λ q, D P, µ D P, µ µ 2 µ, Λ q, D P, µ Λ q µ 2 µ, Λ q, D P, µ D P, µ 2 µ 2 µ, Λ q, D P, µ. D P, µ Λ q Note that the second term of the last expression is always positive. In particular, higher quality realizations generate higher beliefs Λ q, second-period prots are increasing in beliefs and beliefs satisfy the following condition: 2 µ 2µ,Λq,DP,µ DP,µ Λq > 0. The rst term needs more careful explanation. It can be either positive or negative depending on how second-period beliefs are aected by rst-period demand the speed of information diusion through word-of-mouth communication. The overall eect is positive by assumption 1, i.e. marginal prots are increasing in quality. Specically, µ 2 is an increasing function of D P, µ for high quality realizations, since an increase in D P, µ improves the monopolist's reputation and prots when news is good, which in turn is more likely for the high-quality seller. Condition 2 is implied by 2 Πθ,P,µ θ µ > 0: ˆ = q 2 Π θ, P, µ θ µ = {ˆ µ q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ Therefore it is enough to show that π µ 2 µ, Λ q, D P, µ f } θ q θ dq µ 2 µ, Λ q, D P, µ fθ q dq > 0. µ θ 18

19 q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ because of FOSD of f with respect to θ. = Λ q q q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ 2 π µ 2 µ, Λ q, D P, µ 2 µ 2 µ, Λ q, D P, µ Λ q + q π µ2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ µ 2 µ, Λ q, D P, µ > 0 µ µ 2 µ, Λ q, D P, µ µ µ 2 µ, Λ q, D P, µ Λ q µ 2 µ, Λ q, D P, µ µ 2 µ 2 µ, Λ q, D P, µ, µ Λ q which is positive since second-period prots are increasing and convex in beliefs, second-period beliefs are increasing in the quality signal, and the quality signal Λ q is increasing in the observed quality. Moreover second-period beliefs are increasing in µ, directly and trhough its eect on rst-period demand Assumption 1 and satisfy : 2 µ 2µ,Λq,DP,µ µ Λq > 0 an increase in rst-period beliefs µ generates more demand, which in turn makes the quality signal Λ q more informative, and therefore increases its impact on beliefs µ 2 µ, Λ q, D P, µ. Proof of Proposition 6. The proof consists of two steps. We rst show that there is no equilibrium price P < P that satises the intuitive criterion. Consider the price P < P such that P L, P is a separating equilibrium. Dene P = P + ε. Then it is easy to see that a Π H, P, µ = 1 Π H, P, µ = 1 and b Π L, P, µ = 1 < Π L, P L, µ = 0. Let P H be the price that maximizes the high monopolist's prots under the most optimistic beliefs µ = 1, Π H, P, µ = 1. Noting that P H < P H and P H > P > P, we get that P H > P > P. Therefore Π H, P, µ = 1 Π H, P, µ = 1. By Proposition 5 we know that Π L, P, µ = 1 < Π L, P L, µ = 0, then by continuity Π L, P, µ = 1 < Π L, P L, µ = 0. Thus for any price P < P condition a is not satised, violating the intuitive criterion. We now show that P L, P is the only separating equilibrium that satises the intuitive criterion, that is there is no equilibrium price P such that a Π H, P, µ = g Π H, P, µ = g and b Π L, P, µ = g < Π L, P L, µ = b. If P < P condition a is not satised. Then, P P. But if P > P, there is no separating equilibrium, since any deviation at P > P is protable for the low-quality seller, as shown in Proposition 5. Then it must be P = P, and P L, P is the only separating equilibrium that satises the intuitive criterion. Proof of Proposition 7. By Proposition 5, the price P < P H is such that the low-quality monopolist is indierent between following the equilibrium strategy or mimic his high-quality counterpart, Π L, P, µ = 1 = Π L, P L, µ = 0. It is therefore enough to study how the last equality varies with k: 19

20 Π θ = L, P L, µ = 0 k = Π θ = L, P, µ = 1 k { P L D P L, µ = 0 ˆ + π µ 2 k, µ = 0, Λ q, D P L, µ = 0 } f L q dq k q which is equal to: = { P D P, µ = 1 ˆ + π } µ 2 k, µ = 1, Λ q, D P, µ = 1 fl q dq, k q ˆ q π µ 2 k, 0, Λ q, D P L, 0 µ 2 k, 0, Λ q, D P L, 0 µ 2 k, 0, Λ q, D P L, 0 k f L q dq = [P D P, 1 P + D P, 1 ] P k ˆ π [ µ 2 k, 1, Λ q, D P, 1 µ2 k, 1, Λ q, D P, µ 2 q µ 2 k, 1, Λ q, D P, 1 k k, 1, Λ q, D P, 1 D P, 1 D P, 1 P ] P f L q dq k Therefore: P k = q [ πµ 2k,0,Λq,DP L,0 µ 2k,0,Λq,DP L,0 [ DP,1 P + D P, 1 + q P µ 2k,0,Λq,DP L,0 k πµ 2k,1,Λq,DP,1 µ 2k,1,Λq,DP,1 πµ2k,1,λq,dp,1 µ 2k,1,Λq,DP,1 µ 2k,1,Λq,DP,1 DP,1 ] µ 2k,1,Λq,DP,1 k DP,1 P f L q dq ] < 0. f L q dq Note that the equilibrium price P is decreasing in k, since the denominator of the last expression is positive, and the numerator is negative. The denominator is the sum of two terms. The rst one represents the rst-period marginal income, which is positive since the high-quality monopolist is charging a price lower than the monopoly price. The second term is also positive because marginal prots are increasing in q, by Assumption 1 for low quality draws, the overall impact of rst-period demand on second-period beliefs is negative: µ2k,1,λq,dp,1 DP,1 and DP,1 P are both negative since quality is drawn from the lower distribution. The numerator is negative since second-period beliefs are increasing in k, the weight consumers attribute to signaling, when beliefs generated by signaling are the most optimistic, µ = 1; while the contrary occurs for the most pessimistic case, in which µ = 0. 20

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