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Article Excerpt
As is well recognized, market dominance is a typical outcome in markets with network effects. A firm with a larger installed base offers a more attractive product which induces more consumers to buy its product which produces a yet bigger installed base advantage. Such a setting is investigated here but with the main difference that firms have the option of making their products compatible. When firms have similar installed bases, they make their products compatible in order to expand the market. Nevertheless, random forces could result in one firm having a bigger installed base, in which case the larger firm may make its product incompatible. We find that strategic pricing tends to prevent the installed base differential from expanding to the point that incompatibility occurs. This pricing dynamic is able to neutralize increasing returns and avoid the emergence of market dominance.
1. Introduction
* Markets for products with network effects face the following conundrum. The value of the good to consumers is greatest when a single product dominates, as then network effects are maximized. However, the dominance of a single product typically means the presence of a monopoly, in which case consumers suffer the usual welfare losses from an excessively high price.
One possible solution to this conundrum is to have multiple firms offer compatible products. If there is complete compatibility then there are no foregone network effects, and the presence of viable competitors means price competition is operative. In fact, this was the basis for one of the proposed structural remedies in the Microsoft case. Referred to as the Baby Bills solution, the proposal was to divide the Windows monopoly into several identical companies which would initially have compatible (in fact, identical) products. Key to the remedy's appeal is that by initializing the market with compatible products, these newly created competitors would have an incentive to maintain compatibility over time.
For product compatibility to represent a long-run solution to the problem of network effects, two conditions must then be satisfied. First, firms must initially find it in their interests to make their products compatible. Second, there must be incentives to maintain compatibility when, in response to future developments, differences emerge in firms' installed bases.
There are a number of articles that explore the first condition, including Katz and Shapiro (1986), Economides and Flyer (1997), Cremer, Rey, and Tirole (2000), Malueg and Schwartz (2006), and Tran (2006). (2) The standard model is a two-stage structure; in the first stage, firms make compatibility decisions and, given products are or are not compatible, they engage in price or quantity competition (for either one or two periods). Consistent with the Microsoft setting, both firms must agree for their products to be compatible. There are two primary forces that influence whether or not compatibility occurs in equilibrium. First, compatibility enhances the value of firms' products by increasing network effects. As this draws more consumers into the market, firms have a mutual interest in making their products compatible. Second, when firms have different installed bases, the larger firm loses an advantage with compatibility. In contrast, the smaller firm always prefers products to be compatible because it benefits through both effects. Existing work has shown that if firms are not too different--either in terms of installed bases or other traits--then products are compatible.
Having established that there are initial market conditions that would result in firms choosing to make their products compatible, this leads us to the second issue, which is the long-run viability of compatible technologies. Even if firms are initially similar and make their products compatible, randomness in demand and other shocks will surely lead to asymmetric installed bases. Could a modest difference in installed bases induce the current market leader to choose incompatibility in a march toward dominance? If so, then creating a structure with initially compatible products may only delay--but not prevent--increasing returns from kicking in and creating a monopoly. Or are there forces that would maintain incentives for compatibility even when the installed base differential is significant? More generally, are compatible products stable in the long run, or can we expect that eventually market dominance will emerge?
To explore long-run market structure issues when network effects are present, there is a growing body of work, including Mitchell and Skrzypacz (2006), Llobet and Manove (2006), Cabral (2007), Driskill (2007), and Markovich (2008). However, none of these models allow firms to make their products compatible, and thus cannot address the issue of whether compatible products are stable in the long run.
The modelling innovation of this article is to endogenize product compatibility in a dynamic stochastic setting so as to address the long-run market structure of a product market characterized by network effects. In each period, firms first decide on compatibility and then price. Demand and customer turnover are stochastic, which means that firms are very likely to end up with asymmetric installed bases even if they begin identical and choose compatible products. Although consumers are myopic, firms dynamically optimize. A Markov perfect equilibrium is numerically solved for, and we assess the frequency with which market dominance occurs and explore its determinants.
Our main finding is that compatible products can indeed be stable in the long run. What underlies this finding is a dynamic that can neutralize increasing returns and prevent market dominance from emerging. As long as network effects are not too strong, firms that begin with comparably sized installed bases will choose to make their products compatible. Furthermore, if the installed base differential should grow--even to the point that the larger firm makes its product incompatible--the smaller firm prices aggressively so as to reduce the differential and thereby maintain or restore mutual incentives for product compatibility. This pricing dynamic is sufficiently powerful to sustain compatible products in the long run and prevent market dominance from emerging. Interestingly, if a product has stronger network effects, it is possible that this strategic pricing effect is so intensified that it actually becomes more likely that products are compatible.
The model is described in Section 2, and the definition and computation of equilibrium are discussed in Section 3. As a benchmark, Section 4 covers the static Nash equilibrium for the compatibility-price game. Markov perfect equilibria are reviewed in Section 5, and the implications of product compatibility for market dominance are explored in Sections 6 and 7, with the latter focusing on the role of network effects. A welfare analysis of various policy regimes is examined in Section 8, and we conclude in Section 9.
2. Model
* Our objective is to provide some general insight about the long-run stability of compatible technologies in the midst of network effects. Toward that end, we chose not to tailor the model to a specific product--such as operating systems--but rather to develop a more generic model that encompasses the key forces at play in many markets characterized by network effects.
* State space and firm decisions. The model is cast in discrete time with an infinite horizon. Although our attention in this article is limited to when there are just two firms, the model will be described for the more general case of N [greater than or equal to] 2 firms. These firms sell to a sequence of heterogeneous buyers with unit demands. At the start of a period, a firm is endowed with an installed base which represents consumers who have purchased its product in the past. Let [b.sub.i] {0, 1 , ... , M} denote the installed base of firm i at the start of a period where M is the maximal size of the installed base.
Given ([b.sub.1], ..., [b.sub.N]), firms engage in a two-stage decision process in which they choose compatibility in stage 1 and then price in stage 2. In stage 1, each firm decides whether or not to "propose compatibility" with each of the other firms. Let [d.sub.ij] [member of] {0, 1} be the compatibility choice of firm i with respect to firm j, where [d.sub.ij] = 1 means "propose compatibility." To actually achieve compatibility requires that both firms propose it. Thus, the technologies of i and j are "compatible" if and only if [d.sub.ij] * [d.sub.ji] = 1. Requiring both firms to consent is consistent with a number of markets, including those involved in the Microsoft case. Furthermore, the analysis promises to be more interesting than when a firm can, by itself, make its product compatible. (3) After compatibilities are determined, firms simultaneously choose price. Let [p.sub.i] denote the price of firm i.
Although firms can influence compatibility and price, we do not allow interfirm payments which would permit a firm to induce a competitor to make its product compatible through appropriate compensation. This assumption is common in the literature on network effects. Malueg and Schwartz (2006) summarize the arguments in its favor, of which the most compelling is that such payments may not be permitted by the antitrust authority, as they provide fertile grounds for firms to collude.
This is clearly a stylized modelling of compatibility, but should serve our purposes well. Our primary interest is in understanding the incentives for compatibility, and that means learning when firms prefer compatibility. We have then given them maximal flexibility by ignoring any technical constraints and assuming compatibility is costless to change. Furthermore, this modelling approach means that compatibility is not a state variable, and this is important in keeping the dimensionality of the state space manageable. After presenting our main results, we argue that they are likely to be robust to having a cost to changing compatibility.
* Demand. Demand in each period comes from the replacement of a randomly selected old consumer (who previously purchased) with a new consumer. There is one new consumer each period, and her buying decision is based on the following discrete choice model. Let [[epsilon].sub.i] be the idiosyncratic preference of the buyer for firm i's product in the current period. The utility that the consumer gets from buying from firm i is
[v.sub.1] + [theta]g ([b.sub.i] + [lambda] [summation over (j[not equal to]i)] [d.sub.ij][d.sub.ji][b.sub.j]) - [p.sub.i] + [[epsilon].sub.i].
[b.sub.i] + [lambda] [[summation].sub.j[not equal to]i] [d.sub.ij][d.sub.ji][b.sub.j] is the effective installed base of firm i given the set of compatible technologies where [lambda] [member of] [0, 1] allows for the value of the installed base of other compatible technologies to be worth less to consumers of firm i's product, [v.sub.i] is a measure of intrinsic product quality which is assumed to be common across firms: v = [v.sub.i] and is also fixed over time. (4) Network effects are captured by the increasing function [theta]g(x), where [theta] [greater than or equal to] is the parameter that controls the strength of network effects. We will refer to the sum of these two factors, [v.sub.i] + [theta]g(x), as quality. The buyer can also choose to purchase an outside good with utility [v.sub.0] + [[epsilon].sub.0]. As the intrinsic quality parameters only affect demand through the expression [v.sub.0]--v, without loss of generality we set v = 0. The consumer's idiosyncratic preferences ([[epsilon].sub.0], [[epsilon].sub.1], ..., [[epsilon].sub.N]) are unobservable to firms.
A new consumer buys from the firm offering the highest current utility. We are then assuming consumers make myopic decisions (or, equivalently, they have static expectations about the future). By having a parsimonious representation of consumer decision making, we are able to have a rich modelling of firm choice with respect to price and compatibility. An important though challenging extension of our work is to allow consumers to be forward looking with rational expectations. For some recent research along those lines--though not allowing for endogenous compatibility--see Cabral (2007) and Driskill (2007).
Assuming ([[epsilon].sub.0], [[epsilon].sub.1], ..., [[epsilon].sub.N]) are independently extreme value distributed, the probability that firm i makes a sale to a new consumer is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where p is the vector of prices of all firms, d is the vector of compatibility choices, and b is the vector of installed bases. Note that if [v.sub.0] = [infinity] then [[phi].sub.0](p; d, b) = 1 - [[summation].sup.N.sub.i=1] [[phi].sub.i](p; d, b) = 0, so the outside good is hopelessly unattractive and a consumer will buy from one of the N firms with probability one. In that case, expected market demand equals one in each period and, most importantly, is independent of firms' installed bases and any decisions regarding compatibility and price. Those decisions will only influence a firm's expected market share. The case of [v.sub.0] = [infinity] is referred to as the case when market size (or demand) is fixed. When instead [v.sub.0] is not -[infinity], then the expected market size is endogenous. In particular, a firm can increase its expected demand without necessarily decreasing the expected demand of its rivals.
* Network effects and transition probabilities. In modelling network effects, we will assume they are bounded in the sense that g([b.sub.i]) = g(m) if [b.sub.i] [greater than or equal to] m for some m [less than or equal to] M. Bounding the network effect is as specified in Cabral and Riordan (1994), though in their context it was learning by doing. Although the results reported here are based on linear network effects--g([b.sub.i]) = [b.sub.i]/m if [b.sub.i] [less than or equal to] m--we have also allowed g to be convex, concave, and S shaped and the main conclusions of the article are robust.
[DELTA]([b.sub.i]) denotes the probability that the installed base of firm i depreciates by one unit. We specify [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [delta] [member of] [0, 1] is the rate of depreciation. This specification captures the idea that...
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