Strong Nash Implementation And Economic Applications[Mise En Œuvre Selon L’Equilibre De Nash Fort Et Applications Economiques]

Strong Nash implementation is a challenging problem for which there is no similar theorem to that of Maskin (1977/1999) for Nash implementation with simple conditions, which involves a wide range of applications. In this paper, we explore the origins of Maskin's theorem (1979) in this context. We assume that there exists at least one pair of agents who are associated with specific alternatives, which we refer to as separately exclusive alternatives. A pair of agents with separately exclusive alternatives is one where each agent prefers their own alternative over the other agent's alternative, and for each agent, all other agents in society prefer any socially chosen alternative over their respective alternatives. We show that when there are at least three agents, all social choice correspondences satisfying a strong version of Maskin monotonicity and unanimity can be implemented in Nash equilibria. We apply our findings to finite fair allocation problems in matching markets, to infinite fair allocation problems with single-peaked preferences, to efficient sharing Rules for a commonly owned technology and coalitional games.