First Best Bayesian Privatization Mechanisms

A planner is interested in designing an ex-post efficient, individually rational, Bayesian mechanism for allocating a single indivisible object to one of the agents who knows his own valuation and only the distribution of other agents' valuations of the object. In this paper, we show that it is impossible to design such a mechanism without any transfers among agents and the planner. However, we discover and describe an ex-post efficient, ex-post individually rational, Bayesian mechanism which balances transfers among agents without any payment to (or from) the planner. Our result that an ex-post efficient, ex-post individually rational, transfer balanced, Bayesian mechanism exists, is in stark contrast to two well-known impossibility results in the literature; the nonexistence of a Bayesian public good mechanism satisfying expost efficiency, individual rationality and budget balance (Laffont and Maskin (1979)) and the impossibility of an ex-post efficient, individually rational, Bayesian bilateral trading mechanism between a seller and a buyer without an outside subsidy (Myerson and Satterthwaite (1983)).