Individually Rational, Balanced-Budget Bayesian Mechanisms and the Informed Principal Problem

Abstract

We investigate the issue of implementation via individually rational ex-post budget-balanced Bayesian mechanisms. We show that all decision rules generating a nonnegative expected social surplus are implementable if and only if the probability distribution of the agents' types satisfies two conditions: the well-known condition of Cremer and McLean (1985) and the Identifiability condition introduced in this paper. These conditions are also necessary for ex-post efficiency to be attainable. The expected social surplus in these mechanisms can be distributed in any desirable way. The Identifiability condition, as well as Cremer-McLean condition, are generic when there are at least three agents, and none of them has more types than the number of type profiles of the other agents.

Also generically, any ex-post efficient decision rule can be implemented in an informed principal framework, i.e., when the mechanism is offered by an informed participant. Only ex-post efficient mechanisms allocating all surplus to the party designing the mechanism are both sequential equilibrium outcomes and neutral optima, i.e., can never be blocked. Thus, an informed principal can also extract all surplus from the other agents in a Bayesian mechanism.

Keywords: Mechanism design, Bayesian implementation, individual rationality, informed principal

JEL Classification: C72, D82