Mechanism design with set-theoretic beliefs

Abstract

In settings of incomplete information, we put forward: (1) a very conservative - indeed, purely set-theoretic- model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of rationality, capable of leveraging such conservative beliefs. We exemplify the applicability of our new approach for single-good auctions. In particular we show that, under our solution concept, there exists a simple normal-form mechanism, which always sells the good, always has non-negative revenue, and guarantees (up to an arbitrarily small, additive constant) a revenue benchmark that is always greater than or equal to the second-highest valuation, and sometimes much greater. By contrast, we also prove that the same benchmark cannot even be approximated within any positive factor, under classical solution concepts.