A Robustness Result for Rationalizable Implementation

Alfredo Di Tillio published in Games and Economic Behavior

Alfredo Di Tillio (Department of Economics and IGIER) published A Robustness Result for Rationalizable Implementation in Games and Economic Behavior, Volume 72, Issue 1, May 2011, pages 301-305 doi: 10.1016/j.geb.2010.08.001.

Abstract: This paper investigates the extent to which rationalizable implementation depends on the implicit common knowledge restrictions usually embodied in traditional models. It is shown that under fairly general conditions such restrictions are without loss of generality in the following sense: If a mechanism M implements a social choice function f on a type space X, then M implements f assuming only that the agentsʼ k-order beliefs are among those described by an open set B containing X, while higher-order beliefs are completely unrestricted. The result is applied to direct implementation on payoff type spaces, and related to the weak (incentive compatible) implementation problem.