On the Foundations of Ex Post Incentive Compatible Mechanisms

Motivation. The recent literature on mechanism design provides a series of studies on robustness issues, motivated by the idea that a desirable mechanism should not rely too heavily on the agents’ common knowledge structure (Wilson, 1985). One approach is to adopt stronger solution concepts that are insensitive to various common knowledge assumptions, such as dominant-strategy incentive compatibility (e.g., Segal, 2003) and ex post incentive compatibility (e.g., Dasgupta and Maskin, 2000). However, a mechanism that achieves desired outcomes without the agents’ common knowledge assumption does not immediately imply dominant-strategy or ex post incentive compatibility. In revenue maximization in private-value auction, Chung and Ely (2007) fill in this gap by establishing the maxmin and Bayesian foundation of the optimal dominant-strategy mechanism. Consider a situation where the seller in an auction (principal) only knows a joint distribution of the bidders’ (agents) valuation profile for the auctioned object, but does not have reliable information about the bidders’ knowledge of each other’s value. Then dominant-strategy mechanisms have a maxmin foundation if, for any non-dominant-strategy mechanism, there is a possible belief of the seller with which the optimal dominant-strategy mechanism achieves (weakly) higher expected revenue than the non-dominant-strategy mechanism. As a stronger concept, if the same belief can be found for any non-dominant-strategy mechanism with which the optimal dominant-strategy mechanism achieves (weakly) higher expected revenue, then there is a Bayesian foundation.