Mechanism Design with Possibilistic Beliefs

Abstract

We study mechanism design in non-Bayesian settings of incomplete information, when the designer has no information about the players, and the players have arbitrary, heterogeneous, first-order, and possibilistic beliefs about their opponents’ payoff types. Using such beliefs, in auctions of a single good, we

•define a revenue benchmark at least as high as the second-highest valuation, and sometimes much higher;

•prove that it is not meaningfully achievable via traditional notions of implementation; and

•prove that it is achievable via a notion of implementation based only on mutual belief of rationality.