Implementation with Near - Complete Information ∗

Many refinements of Nash equilibrium yield solution correspondences which do not have closed graph in the space of payoffs or information. This has significance for implementation theory, especially under complete information. If a planner is concerned that all equilibria of his mechanism yield a desired outcome, and entertains the possibility that players may have even the slightest uncertainty about payoffs, then the planner should insist on a solution concept with closed graph. We show that this requirement entails substantial restrictions on the set of implementable social choice rules. In particular, when preferences are strict (or more generally, hedonic), while almost any social choice function can be implemented in undominated Nash equilibrium, only monotonic social choice functions can be implemented in the closure of the undominated Nash correspondence. ∗We benefited from conversations with Nabil Al-Najjar and Stephen Morris. Thanks to Eddie Dekel and Mike Whinston for helpful comments and advice. The suggestions of two anonymous referees helped us to improve the exposition of this paper. †[email protected] ‡[email protected]. Financial Support from NSF grant SES 99-85462 is gratefully acknowledged.