Nash implementation and double implementation: equivalence theorems

摘要

This paper contains a full characterization of doubly implementable social choice correspondences (SCC's) in Nash equilibria and undominated Nash equilibria in general environments. We show that in the case of at least three agents, an SCC is doubly implementable if and only if it is Nash implementable. By contrast, for the case of two agents, the class doubly implementable SCC's is strictly smaller than that of Nash implementable SCC's Nonetheless, the equivalence of Nash implementability and double implementability does hold in general environments for any SCC F satisfying a unanimity condition and the mild requirement that for each agent, no F-optimal alternative be worst, We give examples of interesting SCC's that are both Nash implementable and doubly implementable in economic environments.