Conservative Rationalizability and The Second-Knowledge Mechanism

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. ∗This work is funded by the Office of Naval Research under award number N00014091059. (Any opinions, findings, and conclusions or recommendations expressed in this email are those of the author (s) and do not necessarily reflect the views of the Office of Naval Research.)