Absence of Commitment in Principal-Agent Games

The Revelation Principle is the cornerstone of the theory of mechanism design. It shows that seemingly complex problems can be viewed as programming problems with constraints that give the agent the right incentives to truthfully reveal his private information. Needless to say, the theory is widely applicable. Nevertheless, one of the main assumptions underlying the Revelation Principle is not satisfied in many applications. This is the assumption that the Principal can commit to any outcome of the mechanism. If this assumption is not satisfied, the set of outcomes is (usually) significantly smaller. A major advance in the study of Principal-Agent games without commitment is due to Bester and Strausz [3]. They show that even with imperfect commitment, the problem can be reduced to a programming problem, albeit under slightly stronger conditions. Nevertheless, the set of outcomes is (usually) significantly smaller than what could have been obtained if the Principal had been able to commit, or equivalently, there had been a mediator. It should be noted that another advancement due to Bester and Strausz is in formulating the problem so that all cases between perfect commitment and no commitment can be handled simultaneously. However, they rely on only one round of communication. Recently, Aumann and Hart [1] have shown that with repeated communication, the set of equilibrium outcomes can once again be extended and provide a complete characterisation (in terms of bimartingales and biconvexity) of the set of outcomes thus obtained. Once again, the set of outcomes is smaller than the set of outcomes with perfect commitment or a mediator. In this paper, we shall show that we can virtually attain strictly more outcomes even in the absence of a mediator. We draw on the similarities alluded to in Myerson [4], where he shows that noisy communication mechanisms can help agents replace a mediator in games of perfect information (i.e. achieve the set of correlated equilibria) and in Sender-Receiver games. We adapt a mechanism due to Ben-Porath [2] to achieve this. The key to a noisy mechanism, in the case of Sender-Receiver games for example, is the observation that the receiver of a message should not be sure just which type of agent has sent him the message, even after accounting for the fact that the various Sender types may be randomising and using Baye’s rule to update probabilities. This is precisely the service that a mediator provides. We make this precise below. ∗Contact Information: 608, Kern Graduate Building, University Park, PA 16802. Tel: + (814) 237 1280, Email:[email protected]