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Article Excerpt
We consider a model of price competition in a duopoly with product differentiation and network effects. In the efficient allocation, both networks are active and the firm with the highest expected quality has the largest market share. To characterize the equilibrium allocation, we derive necessary and sufficient conditions for uniqueness of the equilibrium of the coordination game played by consumers for given prices. The equilibrium allocation differs from the efficient one for two reasons. First, the equilibrium allocation of consumers to the networks is too balanced, because consumers fail to internalize network externalities. Second, if access to the networks is priced by strategic firms, then the product with the highest expected quality is also the most expensive. This further reduces the asymmetry between market shares and therefore social welfare.
1. Introduction
* Many economic decisions, such as the purchase of a good by a population of consumers, or the adoption of a standard of production by a set of firms, exhibit a specific form of strategic complementarity known as network externality. The set of consumers buying a specific product, and the set of firms producing according to a given standard, constitute virtual networks: the externality arises when the payoff of each player who belongs to a network is increasing in the total size of the network itself.
This article brings two contributions to the literature on network competition. (1) The first contribution is methodological. There is a problem with modelling the demand function for network goods, because the game played by consumers choosing which network to join, after prices have been announced, constitutes a coordination game, and typically these games have multiple equilibria. Therefore, in a basic model of Bertrand competition between identical networks, the demand for each good is not a well-defined function of prices. As a consequence, in order to analyze network competition, it is necessary to select one equilibrium for each of the coordination games that consumers play after observing different price announcements, for example, one that is Pareto efficient, (2) or the one that is the most favorable to one firm, which benefits from a reputation advantage. (3)
Instead, we enrich the basic model by allowing for both horizontal and vertical differentiation, and for incomplete information about the quality of the goods. Rather than complicating the analysis, these more realistic assumptions allow us to derive a well-defined demand function for a large class of markets. In our set-up, consumers' network choices, for given prices, constitute a global game with correlated private values. Therefore, we can derive necessary and sufficient conditions that guarantee the existence of a unique equilibrium of this game and therefore yield a well-defined demand function. These conditions relate to the amount of horizontal differentiation and the quality of the information present on the market.
The second contribution is to address a classic issue in network industries, namely whether the presence of network effects gives rise to excessive or insufficient asymmetry of the market shares of rival firms. In the presence of network effects and product differentiation, characterizing the social optimum is a nontrivial problem: the aggregate surplus from the network effect is maximized if all players join the same network, whereas the surplus from the intrinsic utility from consumption of the good is maximized if every player buys the product he likes the most.
This tradeoff is exemplified by the case of PC and Macintosh. If there was only one standard, every computer owner could run all the existing software and easily exchange files and know-how with anybody else. On the other hand, one of the main reasons why the two standards do coexist is that the two types of computers have different strengths that appeal to the needs of different consumers. (4)
Another example is the case of matrix programming languages. Matlab seems to be best suited to analyze time-series data, whereas Gauss seems to perform better when analyzing panel data (see Rust, 1993). At the same time, all programmers would benefit from the existence of a unique common language because they could exchange suggestions and pieces of code with a larger group of people.
In this article, we investigate this tradeoff between maximizing the aggregated network effect and letting consumers use their favorite product, and show that the market outcome is characterized by insufficient asymmetry of the market shares. This is due to the presence of two sources of inefficiency. The first is that consumers fail to internalize the network externality. The second is that, in equilibrium, the relative price of the high-quality product is too high.
In our model, we assume that two new, alternative network products are introduced and that consumers simultaneously choose which one to join. We consider two cases, one where the networks are "sponsored" and one where the networks are "unsponsored." In the network literature, this distinction refers to the cost an individual bears to join a network: if a network is sponsored, access to it is priced by a strategic firm. If it is unsponsored, access is available at marginal cost. Although most telecommunication networks are typically sponsored, there are many cases of unsponsored networks as well. For example, by learning a new language, an individual can join a "communication network" that clearly exhibits network externalities. In this case, there is no centralized entity that owns the language and strategically sets a price for the access to the network. The "price" is simply the time spent studying the language.
We assume that the goods are both vertically and horizontally differentiated, but neither firms nor consumers can perfectly observe the vertical dimension of quality. More precisely, they observe a noisy public signal about the vertical quality of each good, and one of the two networks has a higher expected quality. Each consumer privately and perfectly observes his private value for each good but he cannot distinguish the common component (the objective quality of the good) from his idiosyncratic taste component. When choosing which network to join, each individual takes into account three elements: his private valuation for each good, the expected size of each network, and the cost he has to bear to join it.
Consider, for example, the introduction of two new, non-interconnected telecommunication networks, such as two kinds of software for videoconference. The assumption of noisy information about the vertical quality of each good captures the fact that the overall performance of such products critically depends on how well they interact with the complementary hardware and software, and this interaction cannot be perfectly tested before the product is introduced. The assumption of horizontal differentiation captures the idiosyncratic taste consumers might have for the more "recreational" features of these products, such as the graphic interface. Finally, the assumption that each consumer perfectly observes his private value for each good before making a purchase captures the fact that software developers typically make trial versions of their products available for free.
We address the question of how the equilibrium allocation of consumers across networks compares to the social optimum. We find that the optimal allocation of consumers across networks is asymmetric, with both networks having positive market shares and more than one half of the population joining the high-quality network. We then look at the allocation implemented by the market, distinguishing between the two cases of sponsored and unsponsored networks.
In the case of unsponsored networks, we identify a first source of inefficiency. Because consumers fail to internalize network effects, the equilibrium allocation is too balanced from a social point of view: the market share of the high-quality firm, although larger than one half, is still smaller than would be socially optimal. This inefficiency is exacerbated as the amount of horizontal differentiation vanishes. Looking at the case of sponsored networks, we find that strategic pricing makes the inefficiency even worse: the high-quality firm has an intrinsic advantage that is reflected in an equilibrium price higher than the one charged by the competitor, and this in turn reduces its market share even more.
A number of papers analyze price competition between two differentiated networks. In models with network effects and pure vertical differentiation, such as the one presented by Farrell and Katz (1998), there are multiple sets of self-fulfilling expectations in the coordination game played by consumers. The same holds for most models where the goods are horizontally differentiated. For example, Griva and Vettas (2004) give a full characterization of the set of equilibria of a model with horizontal differentiation a la Hotelling, allowing also for vertical quality differences.
The closest model to ours is presented by de Palma and Leruth (1993). They allow only for horizontal differentiation and prove that a large degree of heterogeneity in consumers' tastes is necessary and sufficient for uniqueness of the equilibrium. This condition is similar to the condition we derive in our article, for the limit case of our model where all the players perfectly observe the vertical dimension of quality and the latter is identical for the two goods.
Our discussion of the optimal allocation of consumers between networks is related to Farrell and Saloner (1986), who address the issue of whether complete standardization is efficient if consumers have heterogeneous preferences. (5) Our model differs from theirs in that in our model, where heterogeneity in consumers' tastes is modelled as a probit, neither the market equilibrium nor the social optimum can involve complete standardization. In our model, the relevant question is rather what the optimal amount of asymmetry is in the market shares of two networks when there is enough product differentiation to guarantee that both are, and should be, active. More recently, Mitchell and Skrzypacz (2006) have addressed the issue of the optimal amount of disparity in market shares in the long run, in a dynamic model of network competition with product differentiation. In the static version of their model, they find a result similar to ours: the market equilibrium yields more equal market shares than is socially desirable. The main difference between our analysis and the static version of their model is that, whereas they directly assume that the demand function is well defined and downward sloping, we focus on the distribution of consumer preferences and on the information structure of the coordination game they play for given prices, in order to characterize and explain the necessary and sufficient conditions that guarantee that the demand function is well defined and downward sloping.
Finally, Jullien (2001) analyzes network competition with perfect price discrimination and finds a result analogous to the one we establish for the case of sponsored networks: in equilibrium, the largest network is too small. There are two main differences between our model and his. First, in his model, the coordination game played by consumers after prices have been announced has multiple equilibria, and he assumes that consumers always select an equilibrium that maximizes the market share of a given "focal firm." We instead characterize the necessary and sufficient conditions for the existence of a unique equilibrium of the coordination game. Second, he assumes that firms announce prices sequentially (the focal firm first, then its competitor) and can perfectly price discriminate, whereas we assume uniform pricing and simultaneous price announcements.
Our work is also connected to the literature on duopolistic price competition with differentiated goods. For a discussion of...
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