Implementation by mediated equilibrium

Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals’ preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, a mediator coordinates the players’ strategies in a way that discourages deviation. Our main result is a complete characterization of social choice correspondences which are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important social choice correspondences which are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium.