Cheap-talk coordination of entry by privately informed firms.

I analyze and compare the effects of sequential and simultaneous cheap-talk communication (e.g., preannouncement of entry) among privately informed potential entrants who then play a normal-form entry game. The first main result is that cheap-talk communication is powerful enough to enable the potential entrants to coordinate on an efficient outcome for each and every contingency. The second is that sequential cheap talk is more dextrous in this task in the sense that it can generate a greater variety of efficient outcomes than simultaneous cheap talk. The precise extent to which it does so is also explained.

1. Introduction

* Equilibrium entry into an industry that accommodates only a small number of firms (such as natural-monopoly industries) requires a substantial amount of coordination among potential entrants. If the number of firms that can be profitably accommodated varies depending on the entrants' private information (e.g., on their cost efficiency), then even more delicate coordination is needed for efficient entry. Such coordination is too complex to be simply ascribed to the coincidence of beliefs in Nash equilibria; rather, it needs to be pursued consciously by potential entrants. One natural candidate for such endeavor is voluntary exchange of entry intentions and private information. Indeed, we often hear announcements of entry "plans" well before actual entry decisions. These announcements are not binding commitments, and they can be strategically employed, for instance to check the responses of rival firms. As a matter of fact, some of the announced plans are never carried out, possibly discouraged by subsequent announcements of rival plans. As such, these announcements bear the characteristics of cheap talk, that is, they are costless (i.e., do not directly affect the payoffs), (1) unverifiable, and nonbinding. This article reports on an investigation as to how, and to what extent, such communication can improve coordination among potential entrants. It also clarifies the different effects of sequential and simultaneous announcements.

Existing literature on entry coordination focuses on complete-information environments in which the traditional solution is asymmetric Nash equilibria in pure strategies: exactly as many firms as can be accommodated by the market enter. Note that efficiency is obtained in these equilibria even without communication. But there are a large number of such equilibria that are equivalent up to relabelling of the firms, so the question arises whether and how the firms can actually coordinate on one of these equilibria.

Farrell (1987) first studied cheap-talk communication as an attempt to answer this question and showed that simultaneous cheap-talk announcements of entry intentions can enhance the coordination. He also showed that more rounds of such announcements induce further coordination but fall short of achieving full coordination. Rabin (1994) showed, inter alia, that Farrell's coordination effects can be strengthened to a certain extent by "enriching" the language. (2)

In this article I investigate an environment that differs from the existing literature in one important respect: the potential entrants have their own characteristics (types) that are not known to their competitors. I believe that this feature is widely present in many situations of economic interest, such as entry into natural-monopoly industries, patent races, and capacity expansion in concentrated industries. This feature also makes the coordination problem between the firms quite different from that of complete-information cases. To begin with, it is straightforward to see that efficiency cannot be obtained without communication when the entrants have private types: the identities of efficient firms to enter vary contingent upon the types of all firms, but each firm only knows its own type when it makes an entry decision. In contrast to complete-information cases, therefore, communication generates improvements for all firms over and above the no-communication outcome, by inducing coordination on not only the right number but also the right types of firms to enter for each contingency. Note that successful coordination on the latter entails intrinsic asymmetries between firms, although they partly balance out across contingencies. Hence, I find that asymmetric equilibria are normal in this environment, unlike in complete-information models where the firms remain symmetric throughout the game.

I ask how much coordination can be achieved in this environment through the standard means of our daily communication, namely, cheap talk. To address this question I build on the model of Farrell (1987) by letting the potential entrants be privately informed about their productivity, and then analyze and compare the effects of sequential and simultaneous cheap-talk communication that takes place before a normal-form entry game. My first main result is that such cheap-talk communication is powerful enough to enable potential entrants to coordinate on efficient entries for all possible contingencies. (3) The second is that sequential cheap talk is more dexterous in this task in the sense that it can generate a greater variety of efficient outcomes than simultaneous cheap talk. (4)

These findings suggest that nonbinding communication is desirable among privately informed potential entrants, for they can use it to exchange sufficient information to deter inefficient entry. This seems to be consistent with the aforementioned practice of voiding preannouncements, which is indeed documented in an empirical study by Christensen and Caves (1997), who find systematic relationships between the abandonment of preannounced projects and subsequent announcements of rivals' projects in the context of capacity expansion in the pulp and paper industry.

Before proceeding, I shall briefly discuss the relevance of the two modes of communication examined here. The empirical validity of sequential cheap talk is apparent because the alternating exchange of responsive messages is the usual form of our real-life communication. Notwith-standing the recognized pertinence of interactive communication in many situations, (5) the existing literature on cheap talk largely focuses on one-sided or simultaneous messages.

In the absence of private information, however, the difference between sequential and simultaneous cheap talk does not appear essential: since neither kind of cheap-talk announcements affects the payoff-relevant strategic possibilities, their role is limited to pure coordination among multiple Nash equilibria of the underlying entry game. (6)

With private information, on the other hand, an announcement may carry private information about the speaker and hence change the underlying game by resolving some initial uncertainty. Then, subsequent speakers take this newly arrived information into account in their announcements, which is not possible with simultaneous announcements. So, the two modes of communication differ in a more fundamental way in the presence of private information.

I shall now proceed to elaborate the main results of the article. In my model, three firms are potential entrants to a market. Each firm is privately informed about its productivity or type, which is either "good" or "bad." The market "accommodates" (i.e., generates a positive payoff to every firm that enters) up to two entrants if both are good, but only one entrant if bad. (7) The key incentive of firms is that a good firm wants to enter as long as it expects at most one other firm to enter, whereas a bad firm wants to enter only if it expects to be the sole entrant. To better assess the prospects of other entries, the firms may talk about their types before making simultaneous entry decisions. I examine how effective such communication can be in promoting efficiency.

I find that in spite of the completely opposing interests, the firms can coordinate to achieve efficiency in all contingencies: if there is one good firm, then only that firm enters; if at least two firms are good, then exactly two good firms enter; and if all three are bad firms, then only one of them enters. Basically, for these outcomes to obtain, the two firms that enter when all three are good should reveal their types so that the third good firm knows precisely when to stay out, while the firm that enters when all three are bad should disguise its type because otherwise another bad firm would seek a sole entry by masquerading as a good firm. It turns out that, given the market-accommodation condition mentioned above, exchanges of messages arising from such motives of type revelation provide sufficient information for the firms to make efficient entry decisions for each contingency. Conversely, given these entry decisions, such exchanges of messages are optimal.

Note that for the contingencies that all three are of the same type, the identities of the firms do not matter as long as the right number of them enter. So there are various ways of mapping every contingency to an efficient set of firms to enter. I find that if the firms talk sequentially, all such mappings can actually be induced as an equilibrium. On the other hand, when the firms talk simultaneously, only a restricted subclass of them may be induced: these mappings share the feature that the firm that is supposed to enter when all three are bad is supposed to stay out when all three are good.