This paper solves for the set of equilibrium payoffs in bargaining with interdependent values when the informed party makes all offers, as discounting vanishes. The seller of a good is informed of its quality, which affects both his cost and the buyer’s valuation, but the buyer is not. To characterize this payoff set, we derive an upper bound, using mechanism design with limited commitment. We then prove that this upper bound is tight, by showing that all its extreme points are equilibrium payoffs. Our results shed light on the role of different forms of commitment on the bargaining process. In particular, we show that it is the buyer’s inability to commit to a contract before observing the terms of trade that precludes efficiency.
This paper analyzes the optimal provision of incentives in a sequential testing context. In every period the agent can acquire costly information that is relevant to the principal’s decision. Neither the agent’s effort nor the realizations of his signals are observable. First, we assume that the principal and the agent are symmetrically informed at the time of contracting. We construct the optimal mechanism and show that the agent is indifferent in every period between performing the test and sending an uninformative message which continues the relationship. Furthermore, in the first period the agent is indifferent between carrying out his task and sending an uninformative message which ends the relationship immediately. We then characterize the optimal mechanisms when the agent has superior information at the outset of the relationship. The principal prefers to offer different contracts if and only if the agent types are sufficiently diverse. Finally, all agent types benefit from their initial private information.
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 equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) 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.
Keywords: Bayesian games, Communication, Communication equilibrium, Sequential communication equilibrium
The goal of this paper is to introduce communication in a collective choice environment with information acquisition. We concentrate on decision panels that are comprised of agents sharing a common goal and having a joint task. Members of the panel decide whether to acquire costly information or not, preceding the communication stage. We take a mechanism design approach and consider a designer who can choose the size of the decision panel, the procedure by which it selects the collective choice, and the communication protocol by which its members abide prior to casting their individual action choices. We characterize the solution of this extended design problem. We find that the optimal communication protocol in such an environment balances a tradeoff between inducing players to acquire information and extracting the maximal amount of information from them. In particular, the optimal device may lead to suboptimal aggregation of information from a statistical point of view. Furthermore, groups producing the optimal collective decisions are bounded in size. Comparative statics results shed light on the regularities the design solution exhibits. For example, the expected utility of all agents decreases with the cost of private information and increases with its accuracy, but the optimal panel size is not monotonic in the signals’ accuracy.
JEL Classification: D71, D72, and D78
Keywords: Communication, Collective Choice, Mechanism Design, Strategic Voting, Information Acquisition
In this paper we study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize SU(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 SU(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 SU(G) is equal to the set of communication equilibria of G.