Continuous virtual implementation: Complete information

Abstract

A social choice rule (SCR) is a mapping from preference profiles to lotteries over outcomes. When preference profiles are close to being common knowledge among players, an SCR is continuously virtually fully implementable if there exists a mechanism such that all its equilibrium outcomes are arbitrarily close to the outcomes recommended by the SCR. When there are at least three players and a domain condition is satisfied, we obtain the following result: any SCR is continuously virtually fully implementable in Bayesian Nash equilibria, as well as in interim correlated rationalizable strategies, by a finite mechanism.