Mechanism Design with Maxmin Agents: Theory and an Application to Bilateral Trade

This paper studies mechanism design when agents are maxmin expected utility maximizers. The …rst result gives a general necessary condition for a social choice rule to be implementable. The condition combines an inequality version of the standard envelope characterization of payo¤s in quasilinear environments with an approach for relating maxmin agents’ subjective expected utilities to their objective expected utilities under any common prior. The condition is then applied to give an exact characterization of when e¢ cient trade is possible in the bilateral trading problem of Myerson and Satterthwaite (1983), under the assumption that agents know each other’s expected valuation of the good (which is the information structure that emerges when the agents start with a common prior but are pessimistic about how the other agent might acquire information before participating in the mechanism). Whenever e¢ cient trade is possible, it may be implemented by a relatively simple double auction format. For helpful comments, I thank Pierpaolo Battigalli, Aaron Bodoh-Creed, Subir Bose, Gabe Carroll, Aytek Erdil, Ben Golub, Fuhito Kojima, Massimo Marinacci, Paul Milgrom, Suresh Mutuswami, Phil Reny, Ilya Segal, Andy Skrzypacz, Joel Sobel, three anonymous referees, and participants in several seminars. I thank Jason Huang for excellent research assistance.