On the necessary and sufficient conditions for Nash implementation

The purpose of this paper is to provide a constructive way of checking whether or not a social choice correspondence can be implemented in Nash equilibria. The results apply when there are two or more players. The usefulness of this constructive approach is illustrated for the case of single-peaked preferences over , a two-person public good economy with monotonic preferences, and a two-person exchange economy with monotonic preferences.I am grateful to Rajeev Bhattacharya, William Thomson, Takehiko Yamato, and an anonymous referee, for helpful comments. This research was supported by grants from the Bank of Sweden Tercentenary Foundation and the Royal Swedish Academy of Sciences.