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Description
In a dynamic game of investment in product quality, I investigate whether collusive underinvestment equilibria can be supported by the threat of escalation in investment outlays. When there are no spillovers, underinvestment equilibria exist even though, by deviating, a firm can gain a persistent strategic advantage. When there are strong spillovers, underinvestment equilibria fail to exist. A weakening of patent protection can thus lead to more investment in equilibrium. A "nonfragmentation" result is shown to hold: in all free-entry equilibria, industry concentration is bounded away from zero, no matter how large the market, and despite the existence of underinvestment equilibria.
1. Introduction
* In recent years, antitrust authorities have devoted much of their attention and resources to fast-growing innovative industries such as computing, pharmaceuticals, and healthcare. (1) In these cases, the complaint often explicitly focuses on the dynamic nature of competition in such markets. As Evans and Schmalensee (2001) point out, static price/output competition in the market is arguably less important in innovative industries than dynamic competition for the market. In such industries, antitrust authorities should thus be more concerned with adverse effects on investment and innovation rather than on prices or quantities.
This article is concerned with collusion in investment levels in industries in which firms invest to improve their product quality. Indeed, oligopolistic firms often invest in order to gain a competitive advantage over their rivals, and thereby impose a negative externality on their rivals. Because of this business-stealing effect, noncooperative investment levels tend to be higher than those that maximize firms' joint profits. Hence, firms have an incentive to coordinate on low investment outlays. Such underinvestment may be sustained by the threat of an escalation in investment outlays in the event of a deviation.
While a number of articles take seriously the fact that competition in innovative industries is dynamic in nature, the literature has so far ignored the possibility of collusion in investment levels. On the other hand, the existing literature on collusion focuses exclusively on collusion in transitory economic variables such as prices and quantities. This article takes a step towards integrating these two approaches and so providing a tool for analyzing competition in such dynamic markets.
In innovative industries, endogenous industry dynamics are important in that current investments in product or process innovation change not only current but also future market conditions. Since it is difficult for a firm to "unlearn" the result of its investments in quality, these investments have a permanent impact on firms' payoffs. This suggests that one should model dynamic competition in product quality as a dynamic investment game rather than as an infinitely repeated game since, in the latter, tangible market conditions are assumed to be stationary.
While there is a large literature on collusion in infinitely repeated games, dynamic investment games--in which current actions have tangible effects on future payoffs--are much less well understood. From a series of folk theorems it is well known that collusive equilibria exist in infinitely repeated games, provided the discount factor is sufficiently large. In a dynamic investment game, however, a deviant firm can change future market conditions by outspending its rivals and thereby gain a persistent strategic advantage. The existence of tacitly collusive underinvestment equilibria in dynamic investment games is therefore not obviously ensured.
In this article, I analyze a dynamic game of investment in product quality. Such investment might be thought of as quality-improving R&D (e.g., Sutton, 1998) or as persuasive advertising (e.g., Sutton, 1991). I find that the existence of underinvestment equilibria depends crucially on the presence of spillover effects in the appropriation of the benefits from investment. When there are no spillovers from investment, underinvestment equilibria exist as long as the investment cost function is sufficiently elastic, and the discount factor sufficiently large. However, when there are strong spillovers, underinvestment equilibria fail to exist, even for discount factors arbitrarily close to unity. To the extent that an increase in patent protection reduces spillovers from investment, stronger patent protection may paradoxically result in less investment in equilibrium. The reason is that firms have less incentive to invest when they cannot fully appropriate the benefits, and this reduction in the incentives to invest destroys the punishment mechanism through which underinvestment is supported in equilibrium. This should be of concern for antitrust authorities since, as I show, underinvestment unambiguously reduces welfare.
On the positive side, the existence of underinvestment equilibria in my model (when there are no spillovers) raises an important question for the analysis of market structure. Since R&D- and advertising-intensive industries are "endogenous sunk cost" industries (Sutton, 1991), the question arises whether the "finiteness property" or "nonfragmentation result" (Shaked and Sutton, 1987) holds in my dynamic investment game; that is, whether or not in any free entry equilibrium, the number of active firms remains finite, even as the market grows without bound.
Yet competition in endogenous sunk cost industries is dynamic in nature, and the nonfragmentation result has been obtained solely in static stage-game models. It is an open question whether this result still holds in dynamic models. In a static model, the finiteness property is proved by showing that there always exists a profitable deviation for some firm in a large and fragmented market. This deviation consists of a sufficient rise in investment outlays so as to capture a positive market share. In a dynamic model, however, such a single deviation might be followed by a severe (and possibly complex) "punishment" strategy by rival firms, making the deviation potentially unprofitable. Thus it is not clear whether the finiteness property will still hold in cases where underinvestment equilibria can be sustained through such punishment strategies. Nevertheless I am able to show that the result is indeed robust: in all equilibria of my dynamic investment game, the number of firms must remain finite--there is a lower bound to concentration in such dynamic markets.
* Related literature. In addition to Sutton's work on industrial market structure (Shaked and Sutton, 1987; Sutton, 1991, 1998, forthcoming), this article is related to the literature on dynamic investment games in industrial organization; see, for example, Reinganum (1989), Segal and Whinston (2003) on dynamic R&D; Budd, Harris, and Vickers (1993) and Cabral and Riordan (1994) on increasing dominance. This literature has widely ignored the possibility of tacit collusion in investment levels, sustained by the threat of an escalation in investment outlays. A notable exception is the model of investment in capacity by Fudenberg and Tirole (1983). (2) But in their continuous-time game the existence of underinvestment equilibria is trivially ensured (even for arbitrarily small discount factors) since, by construction, a deviant firm cannot leapfrog its rivals and therefore never get a persistent strategic advantage. Moreover, as I will discuss, there is a subtle but important difference between sustaining underinvestment in capacity and underinvestment in product quality, which is closely connected to Sutton's (1991) distinction between "exogenous" and "endogenous" sunk cost industries. Once a firm has sufficient capacity to flood the entire market, it has no incentive to build more capacity, no matter how large the discount factor, and so capacity costs become less and less important (relative to revenues) as the discount factor becomes large. In contrast, since consumers always prefer higher-quality products to lower-quality products, noncooperative incentives to invest in quality increase without bound as the discount factor becomes large. This implies that the threat of escalation in investment outlays--which is used to sustain collusive underinvestment--becomes larger, the larger is the discount factor. Consequently, it is possible to sustain collusive underinvestment in quality even though by deviating a firm can get a persistent strategic advantage over its rivals. This article thus shows that it is not innocuous to lump together different types of dynamic games under the general heading "dynamic investment games." Building on the framework developed by Ericson and Pakes (1995), there is also a recent and growing literature that analyzes industry dynamics using numerical methods; e.g., Gowrisankaran (1999) on horizontal mergers, Besanko and Doraszelski (2004) on capacity investment, and Doraszelski and Markovich (2005) on advertising. Restricting attention to Markov-perfect equilibria, this literature does not consider collusion. Two recent exceptions are Fershtman and Pakes (2000) and de Roos (2004). However, these authors analyze collusion in transitory economic variables (prices or quantities) that do not affect tangible market conditions, and they therefore need to introduce an extraneous state variable that indicates whether a firm has deviated in the past. Building on Fudenberg and Tirole (1983), I show that collusion in investment levels can be sustained even when restricting attention to Markov-perfect equilibria, and even without artificially expanding the state space.
The article is laid out as follows. In Section 2, I present the basic two-firm version of the model when there are no spillovers. The noncollusive benchmark equilibrium and the existence of collusive underinvestment equilibria are analyzed in Section 3. In Section 4, I compare welfare in the different types of equilibria. In Section 5, I introduce spillovers into the model, and re-visit the existence of collusive underinvestment equilibria. In Section 6, I turn to the analysis of market structure, and investigate whether the two-firm underinvestment equilibria are stable with respect to further entry, independently of market size and entry costs. In Section 7, I analyze whether the finiteness property holds in the dynamic game, despite the existence of underinvestment equilibria. Finally, Section 8 concludes. Proofs not found in the Appendix can be found at the Web Appendix (www.rje.org/main/sup-matl.html).
2. The basic model
* In this section, I present the basic dynamic model without spillovers. There are two firms, each offering one variety of a quality good. In each period, firms first decide how much to invest. Then, they compete in quantities. A firm's investment persistently raises consumers' willingness-to-pay for the firm's offering, and so improves the firm's competitive position relative to that of its rival. Under my preferred interpretation (which I will henceforth adopt), investment is in quality-improving R&D (with deterministic outcome) as, for example, in Sutton (1998). Under my alternative interpretation, which the reader may keep in mind, investment is in persuasive advertising or in the stock of "goodwill." (3) In this section, I do not allow for entry of a third firm. The topic of potential entry, which is essential for the analysis of market structure, will be taken up in Sections 6 and 7.
Consider a dynamic infinite-horizon version of Sutton's (1991) model of investment in product quality. Time is discrete and indexed by t. There are two firms, i = 1, 2, and N consumers indexed by l. Consumer preferences are defined over a quality good, produced in the industry under consideration, and an 'outside good' (or Hicksian composite commodity) whose price and attributes are assumed to be constant over time. There are two varieties of the quality good on offer, one by each firm. Consumers value quality. Specifically, consumer l's utility in period t is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
otherwise,
where [x.sup.l,i.sub.t] [greater than or equal to] and [y.sup.l.sub.t] [greater than or equal to] are the quantities consumed of firm i's variety of the quality good and the outside good, respectively; [u.sup.i.sub.t] is the quality of firm i's offering in period t, and [[alpha].sup.l] > is a parameter that measures the intensity of consumer l's preferences for the quality good. Consumer income in each period is denoted by [m.sup.l]. I assume [m.sup.l] > [[alpha].sup.l], which ensures that each consumer l consumes a positive amount of the outside good. The quality index is normalized so that the basic version of the quality good is of quality 1, i.e., [u.sup.i.sub.t] [greater than or equal to] 1. Note that, for [x.sup.l,i.sub.t] > 0, utility is strictly increasing in quality [u.sup.i.sub.t].
In the quality good industry, firm i's period-t cost of investment in quality improvement is given by
F([u.sup.i.sub.t]; [u.sup.i.sub.t-1]) = [F.sub.0][([u.sup.i.sub.t]).sup.[beta]] - [F.sub.0] [([u.sup.i.sub.t-1]).sup.[beta]], (2)
where [F.sub.0] > and [beta] [greater than or equal to] 2 are parameters that measure the effectiveness of spending in raising consumers' willingness-to-pay. (The assumption [beta] [greater than or equal to] 2 ensures that the firm's investment problem is well behaved.) Without loss of generality, normalize the cost parameter [F.sub.0] [equivalent to] 1. The effectiveness of quality investment is subject to diminishing returns; there are no "adjustment costs." Observe that F(u; u) = 0: investment costs are zero if a firm does not raise the quality of its product. Further, assume that quality does not depreciate, and [u.sup.i.sub.t] [greater than or equal to] [u.sup.i.sub.t-1]. Both firms have constant and strictly positive marginal costs of production, c > 0, which are independent of quality.
The timing of the game is as follows. In each period, there are two stages. In the first stage, firms 1 and 2 simultaneously decide whether and how much to invest in quality improvement, and incur the fixed investment outlays. In the second stage, the two firms simultaneously decide how much to produce (quantity competition); consumers, taking price as given, decide how much to consume of each product, and prices are such that markets clear. Firm i's second-stage profit in period t is therefore given by ([p.sup.i.sub.t] - c)[x.sup.i.sub.t], where [p.sup.i.sub.t] and [x.sup.i.sub.t] are price and quantity, respectively; firm i's net profit in period t is then ([p.sup.i.sub.t] - c)[x.sup.i.sub.t] - F([u.sup.i.sub.t]; [u.sup.i.sub.t-1]).
Consumers maximize the discounted value of per-period utility, taking the sequence of prices and qualities as given. There is no saving or storing. Consequently, consumers' decision problem simplifies to myopic period-by-period utility maximization. Firms maximize the discounted sum of profits. The common discount factor is denoted by [delta] [member of] (0, 1). All parameters of the model, and all moves in past periods and stages, are assumed to be common knowledge.
In the equilibrium analysis, I confine attention to Markov strategies that depend on the tangible state only, and so the relevant solution concept is that of Markov perfect equilibrium (MPE). Recall that every MPE is a subgame-perfect equilibrium (SPE), even when strategies are not restricted to be Markov. The idea of this approach is that history should influence current actions only if it has a direct effect on the current environment, but not because players... |
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