Mechanism Design with Possibilistic Beliefs∗

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