پویایی های سهم بازار در یک مدل انحصار دوگانه ارتباطات شفاهی
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|14534||2014||29 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Games and Economic Behavior, Volume 83, January 2014, Pages 178–206
We analyze dynamic price competition in a homogeneous goods duopoly, where consumers exchange information via word-of-mouth communication. A fraction of consumers, who do not learn any new information, remain locked-in at their previous supplier in each period. We analyze Markov perfect equilibria in which firms use mixed pricing strategies. Market share dynamics are driven by the endogenous price dispersion. Depending on the parameters, we obtain different ‘classes’ of dynamics. When firms are impatient, there is a tendency towards equal market shares. When firms are patient, there are extended intervals of market dominance, interrupted by sudden changes in the leadership position.
Consider a market in which consumers can learn about the available products and their prices in two ways: via own experiences from previous purchases and by asking fellow consumers about products or suppliers. Such gathering of infor- mation via word-of-mouth communication is often a costless byproduct of social interaction, but is unlikely to reveal all decision-relevant information to all consumers in any market. The lack of information may then lead to stickiness in the demand. In this paper we study the dynamics of prices and market shares in a homogeneous-goods duopoly with sticky demand stemming from imperfect word-of-mouth communication. While firms act as perfectly rational forward-looking profit maximizers, consumers behave in a simple fashion. Whenever they learn about the prices charged by both suppliers, they purchase the good from the firm that charges the lower price in that period. If a consumer does not discover the price charged by the alternative supplier via word-of-mouth, then she remains locked-in and returns to the supplier visited in the previous period. 1 As a result of the sticky demand, the firm’s strategic decisions become dependent on its customer base. A central question in the analysis of dynamic oligopoly games is whether market shares tend to equalize over time, or whe ther a firm may be able to build up and subsequently defend a dominant market position persistently. Two basic effects determine whether persistent dominance is likely to occur. On the one hand, having a large customer base implies moremonopoly power over locked-in consumers, which firms tend to exploit by charging higher prices ( anti-competitive effect ). This leads to a tendency towards equal market shares. On the other hand, charging a low price today increases the future customer base. If this incentive is sufficiently strong, then a firm that already has a dominant position in the market, may price very aggressively whenever it is threatened, in order to defend its dominant position ( pro-competitive effect ). This, in turn, leads to a tendency towards extreme market shares. The main contribution of this paper is that it provides a simple framework that does not rely on external shocks but is s till able to explain surprisingly rich dynamics, including a tendency towards equal market shares, as well as persistence of dominance and changes in the role of the dominant firm. The prevalence of word-of-mouth communication plays a key role in the determination of firms’ incentives to build up and subsequently to defend a dominant market position. We thus identify different ‘types’ of dynamics, and relate them to the basic parameters of the model, in particular the discount rate, and parameters that determine the effectiveness of word-of-mouth communication. Our model helps to explain why a firm that has dominated a market for a long period of time, may lose this position again, in which case the competitor takes over the dominant position. In our model, dynamics never ‘die out’, even though we do not assume any exogenous source of uncertainty. As pointed out by Sutton (2007, p. 223) , Markovian models “... are often thought of as being unsatisfactory, on the grounds that they do not treat changes in firms’ shares as an outcome of strategic interactions (maximizing behavior) in marketing, R&D, etc., but rather as the outcome of ‘stochastic shocks’.” Nevertheless, in this paper we provide a framework, where the dynamics are driven only by strategic interaction between the firms, namely via the use of mixed pricing strategies in the Markov perfect equilibria. The endogenous price dispersion then determines the probability of each firm to gain or lose markets shares, depending on the current state represented by the customer base. Similarly as in Varian (1980) ,firmsadopt randomized pricing strategies in order to be unpredictable to the competitor. As Varian (1980) argues, randomized pricing can be interpreted as limited-time sales that do not exhibit any systematic patterns. Such behavior can be observed for grocery stores or supermarkets, that frequently offer a few selected products at discounted prices. Empirical evidence for price dispersion is provided, for instance, by Lach (2002) , who uses a dataset involving homogeneous products sold by different sellers. Lach (2002, p. 444) also argues that the identified price dispersion is consistent with randomized prices (or sales) as studied by Varian (1980) . In this paper, we extend the idea of sales to dynamic pricing games, and demonstrate how mixed-strategy equilibria can g enerate plausible dynamics. We also relate the dynamic properties to the primitives of the model, namely the information exchange technology and the discount factor. In particular, we identify a tendency towards skewed market share splits when future profits are important. This tendency becomes more pronounced when many consumers rely on word-of-mouth communication. As a distinctive consequence of word-of-mouth communication, a firm with a smaller customer base can attract less additional demand when charging a lower price in the market, because there are fewer consumers who can share this information. As a result, market shares are more sticky near the extremes of the market share space than in the center, where information spreads more efficiently. A firm that has reached a dominant position in the market can then easily defend this position against the smaller competitor whenever it is at stake (pro-competitive effect). This is indeed the case when future profits are sufficiently important and market shares are skewed but not extreme. The firm with a larger customer base then starts to price aggressively and tends to gain market shares. On the other hand, when market shares are closer to one of the extremes, the opposite (anti-competitive) effect dominates: the firm with the larger customer base now prefers to exploit the locked-in consumers in its customer base by charging higher prices. The combination of these two effects often induces a zig-zag pattern near one of the extremes of the market share space, with one firm dominating the market for many consecutive periods. This persistence of dominance, however, can be interrupted by sudden changes in the leadership position. In contrast, when few consumers rely on word-of-mouth and most consumers are fully informed, market shares are very volatile and the role of the leader changes frequently. In this case, the size of the discount factor has little impact upon the dynamics. From the technical point of view, we offer a new treatment of Markov perfect equilibria in mixed strategies. Via a discr etization of the state space, we are able to approximate the evolution of market shares, allowing us to derive analytical results. For a certain range of parameter values where word-of-mouth communication plays a major role in consumers’ information acquisition, we show that a particularly simple market share grid represents market share dynamics sufficiently well.
نتیجه گیری انگلیسی
This paper presents a model of the dynamics of a duopoly, in which dynamics are generated by the firms’ usage of mixed pricing strategies. We demonstrate that with a small set of assumptions, surprisingly rich dynamics are obtained. Depending on the parameter values, our model can generate dynamics where market shares tend to equalize over time, as well as dynamics where dominance persists over many consecutive periods. In dynamic duopoly models, the state often tends to evolve into a direction where the joint payoff increases. 49 In our model, the joint (expected) payoff in the myopic case is higher when market shares are skewed, because the firm with a larger customer base then tends to price less aggressively. One may, therefore, suspect that market shares would become more skewed when future profits are more important. Our results confirm this prediction. Depending on the amount of word-of-mouth communication as well as on the discount factor, different ‘classes’ of dynamics are obtained in our model. When most consumers are informed, market shares are very volatile, and firms have little incentive to invest in the size of their customer base. The discount factor, then, does not strongly affect the dynamics. When word-of-mouth plays a major role in consumers’ information acquisition, market shares tend to become less volatile. If the discount factor is sufficiently large, they rarely cross the center of the market share space, and extended periods of dominance, interrupted by sudden changes in the leadership position, are obtained. Intuitively, when future profits are important, a firm that has reached a dominant position in the market, defends this position vigorously whenever it is at stake. Conversely, near the extremes of the market share space, the larger firm’s incentive to exploit the locked-in consumers in its customer base dominatesThese two effects explain why a zig-zag pattern of market shares near the extremes is often observed in our model when the discount factor is sufficiently large and word-of-mouth communication is important. Finally, let us briefly revisit some of our assumptions. If our assumption of homogeneous goods is relaxed, a larger firm’s desir e to undercut the competitor’s price in order to defend its dominant market position may be reduced, if product dif- ferentiation gives firms some monopoly power irrespective of past market shares. Therefore, product differentiation may weaken some of our effects. Similarly, the size of the price differential could, in addition to just the ranking of prices, also matter for consumers’ choices. This feature seems relevant for some markets, and may generate dynamics that are less volatile than in our model. Another interesting starting point for future research would be the introduction of forward- looking consumers (e.g., Cabral, 2011 ). In our model, consumers who become informed about both prices always choose the supplier with the lower price. Such a behavior may be suboptimal, if this firm is expected to charge higher prices in future periods