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We consider multi-stage games, where at each stage, players receive private signals about past and current states, past actions and past signals, and choose actions. We fully characterize the distributions over actions, states, and signals that obtain in any (sequential) communication equilibrium of any expansion of multi-stage games, i.e., when players can receive additional signals about past and current states, past actions, and past and current signals (including the additional past signals). We interpret our results as revelation principles for information design problems. We apply our characterization to bilateral bargaining problems.

International audience; This paper considers a general model of repeated games with incomplete information and imperfect monitoring. We study belief-free communication equilibria (BFCE) defined as follows. Players communicate with a mediator who receives types and signals and recommends actions. A BFCE is a communication device such that all players have an incentive to play faithfully, irrespectively of their belief about the state. We characterize BFCE payoffs for any repeated game with incomplete information in terms of one-shot payoff functions, information, and signaling structure.

This paper analyzes the issue of implementing correlated and communication equilibria when pre-play communication is restricted to a particular network (e.g., a hierarchy). When communication between the mediator and the players is not direct and private, as assumed when invoking the revelation principle, there may be incentives for other players in the network to misbehave during the communication phase while players report their private information to the mediator and the mediator sends suggested actions to the players. To remedy this issue, we provide necessary and sufficient conditions on the topology of the network of communication such that restricting communication between the mediator and the players to a particular network does not restrict the set of (communication equilibrium) outcomes that could otherwise be achieved. We show that for any underlying game and any equilibrium outcome available when communication is direct, there exists a communication scheme restricted to a particular network that implements all such outcomes (i.e., does not induce players to deviate in the communication phase) if and only if that network satisfies our conditions.

This thesis consists of three essays in the areas of political economy and game theory, unified by their focus on the effects of pre-play communication on equilibrium outcomes. Communication is fundamental to elections. Chapter 2 extends canonical voter turnout models, where citizens, divided into two competing parties, choose between costly voting and abstaining, to include any form of communication, and characterizes the resulting set of Aumann's correlated equilibria. In contrast to previous research, high-turnout equilibria exist in large electorates and uncertain environments. This difference arises because communication can coordinate behavior in such a way that citizens find it incentive compatible to follow their correlated signals to vote more. The equilibria have expected turnout of at least twice the size of the minority for a wide range of positive voting costs. In Chapter 3 I introduce a new equilibrium concept, called subcorrelated equilibrium, which fills the gap between Nash and correlated equilibrium, extending the latter to multiple mediators. Subcommunication equilibrium similarly extends communication equilibrium for incomplete information games. I explore the properties of these solutions and establish an equivalence between a subset of subcommunication equilibria and Myerson's quasi-principals' equilibria. I characterize an upper bound on expected turnout supported by subcorrelated equilibrium in the turnout game. Chapter 4, co-authored with Thomas Palfrey, reports a new study of the effect of communication on voter turnout using a laboratory experiment. Before voting occurs, subjects may engage in various kinds of pre-play communication through computers. We study three communication treatments: No Communication, a control; Public Communication, where voters exchange public messages with all other voters, and Party Communication, where messages are exchanged only within one's own party. Our results point to a strong interaction effect between the form of communication and the voting cost. With a low voting cost, party communication increases turnout, while public communication decreases turnout. The data are consistent with correlated equilibrium play. With a high voting cost, public communication increases turnout. With communication, we find essentially no support for the standard Nash equilibrium turnout predictions.

In this paper we study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^{U}(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^{U}(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e. all profiles of types have positive probability), then S^{U}(G) is equal to the set of communication equilibria of G.

We analyze a class of sender-receiver games with quadratic payoffs, which includes the communication games in Alonso, Dessein and Matouschek (2008) and Rantakari (2008) as special cases, for which the receiver's maximum expected payoff when players have access to arbitrary, mediated communication protocols is attained in one-round of face-to-face, unmediated cheap talk. This result is based on the existence for these games of a communication equilibrium with an infinite number of partitions of the state space. We provide explicit expressions for the maximum expected payoff of the receiver, and illustrate its use by deriving new comparative statics of the quality of optimal communication. For instance, a shift in the underlying uncertainty that reduces expected conflict can worsen the quality of communication.

We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a pos-sibly infinitely long (but in equilibrium almost surely finite), direct, cheap talk.

International audience; This paper studies extensive form games with public information where all players have the same information at each point in time. We prove that when there are at least three players, all communication equilibrium payoffs can be obtained by unmediated cheap-talk procedures. The result encompasses repeated games and stochastic games.

We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a pos-sibly infinitely long (but in equilibrium almost surely finite), direct, cheap talk.

In a correlated equilibrium, the players' choice of actions is affected by random, correlated messages that they receive from an outside source, or mechanism. This allows for more equilibrium outcomes than without such messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also convey information about the types of the other players, either because they reflect extraneous events that affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Thus, mechanisms can be classified by the connections between the messages that the players receive and their own and the other players' types, the dependence or independence of the messages, and whether randomness is involved. These properties may affect the achievable equilibrium outcomes, i.e., the payoffs and joint distributions of type and action profiles. Whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the number is 14-15 for correlated equilibria and 15-17 for communication equilibria. Each class is characterized by the properties of the mechanisms that implement its members. The majority of these classes have not been described before.

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential communication equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson [Myerson, R.B., 1986. Multistage games with communication. Econometrica 54, 323–358] in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games.

Lehrer and Sorin (1997, Games Econ. Behav. 20, 131–148) use a one-shot public mediated talk model to show that, given any probability distribution on the outcomes of a finite normal-form game, there exists a public mediated talk mechanism that simulates that distribution, provided the probabilities on outcomes are rational numbers. It is shown here that a minor amendment of the very same model allows a much stronger conclusion: any distribution on the outcomes, whether the probabilities are rational numbers or not, can be obtained as the outcome of a one-shot public mediated talk mechanism.

We define a newstrategic equilibrium concept - called strong collusion-proof contract - designed to characterize stable communication agreements in games with differential information against non-binding, selfenforcing and incentive compatible deviations by coalitions. We then construct a strategic market mechanism which, for quasi-linear economies, is such that its strong collusion-proof contracts generically induce the incentive compatible interim efficent allocations. Moreover, it is such that these allocations can be achieved by strong collusion-proof contracts. We show that the internally consistent extension of the strong collusion-proof contracts generically yields the same set of efficent allocations.

This paper offers a new type of explanation for economic institutions as playing the role of mediators in the sense of Myerson (1985) to facilitate communication in contracting settings with ex ante asymmetric information and limited commitment. It derives necessary and sufficient conditions under which mediation is strictly helpful and provides a straightforward, yet general intuition for this result. As an application of our idea we explain the widely observed use of consultants during the restructure of firms.