Conservative Rationalizability and The Second-Knowledge Mechanism

Abstract

In mechanism design, the traditional way of modeling the players' incomplete information about their opponents is "assuming a Bayesian." This assumption, however, is very strong and does not hold in many real applications. Accordingly, we put forward (1) a set-theoretic way to model the knowledge that a player might have about his opponents, and (2) a new class of mechanisms capable of leveraging such more conservative knowledge in a robust way. In auctions of a single good, we show that such a new mechanism can perfectly guarantee a revenue benchmark (always lying in between the second highest and the highest valuation) that no classical mechanism can even approximate in any robust way.