Maximally Informative Decision Rules In a Two-Person Decision Problem

This paper studies how much information can be revealed when agents with private information lack commitment to actions in a given mechanism as well as to the mechanism itself. In a two-person decision problem, agents are allowed to hold on to an outcome in one mechanism while they play another mechanism and learn new information. Formally, decision rule is maximally informative if it is (i) posterior im-plementable and (ii) robust to a posterior proposal of another posterior implementable decision rule. Focusing on a two-person problem, we identify environments where maximally informative decision rules exist. We also show that a maximally informative decision rule must be implemented by a mechanism with a small number of actions (at most 5 for two agents). The result indicates that lack of commitment to a mechanism signi?cantly reduces the amount of information revelation in equilibrium. Keywords: Information aggregation, Limited commitment, Posterior e¢ ciency, Posterior implementation, Renegotiation-proofness.