Unmediated Communication in Games with Complete and Incomplete Information

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.Communication, Correlated equilibrium, Communication equilibrium, Sequential equilibrium, Mechanism design, Revelation principle

Costly Expertise

In many environments, expertise is costly. Costs can manifest themselves in numerous ways, ranging from the time that is required for a financial consultant to study companies’ performances, to the resources necessary for academic referees to produce knowledgeable reports, to the attention and thought needed for jurors to construct informed convictions. The current paper asks a natural question germane to such contexts: how should a committee of potential experts be designed, in terms of the number of participants, their a priori preferences, as well as the rules by which their recommendations are aggregated into a collective policy? We consider a model in which a principal makes a binary decision (e.g., continue or abort a project), the value of which depends on the realization of some underlying state that is unknown (say, whether the project is great or inferior). The principal can hire a committee of experts from a pool varying in their preferences. All experts have access to an information technology providing (public) information regarding the underlying state. Information comes at a private cost to the experts, who care both about the final decision the principal takes, and about the amount they had personally spent on information acquisition

Information Acquisition in Committees

The goal of this paper is to illustrate the significance of information acquisition in mechanism design. We provide a stark example of a mechanism design problem in a collective choice environment with information acquisition. We concentrate on committees that are comprised of agents sharing a common goal and having a joint task. Members of the committee decide whether to acquire costly information or not at the outset and are then asked to report their private information. The designer can choose the size of the committee, as well as the procedure by which it selects the collective choice, i.e., the correspondence between agents’ reports and distributions over collective choices. We show that the ex-ante optimal device may be ex-post inefficient, i.e., lead to suboptimal aggregation of information from a statistical point of view. For particular classes of parameters, we describe the full structure of the optimal mechanisms.Collective choice, Mechanism design, Information acquisition

A Principal-Agent Model of Sequential Testing

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.Dynamic Mechanism Design, Information Acquisition, Sequential Testing.

A Principal-Agent Model of Sequential Testing

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.Dynamic mechanism design, Information acquisition, Sequential testing

Committee Design in the Presence of Communication

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.Communication, Collective Choice, Mechanism Design, Strategic Voting, Information Acquisition

Sequential Equilibria in Bayesian Games with Communication

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.Bayesian games, Communication, Communication equilibrium, Sequential communication equilibrium

Aggregation of Expert Opinions

Conflicts of interest arise between a decision maker and agents who have information pertinent to the problem because of differences in their preferences over outcomes. We show how the decision maker can extract the information by distorting the decisions that will be taken, and show that only slight distortions will be necessary when agents are "informationally small." We further show that as the number of informed agents becomes large the necessary distortion goes to zero. We argue that the particular mechanisms analyzed are substantially less demanding informationally than those typically employed in implementation and virtual implementation. In particular, the equilibria we analyze are "conditionally" dominant strategy in a precise sense. Further, the mechanisms are immune to manipulation by small groups of agents.Information Aggregation, Mechanism Design, Incomplete Information