Nash Implementation Using Undominated Strategies

Abstract

This paper provides a characterization of fully implementable outcomes using undominated Nash equilibrium, i.e. a Nash equilibrium in which no one uses a weakly dominated strategy. The analysis is conducted in general domains in which agents have complete information. Our main result is that with at least three agents any social choice function or correspondence obeying the usual no veto power condition is implementable unless some players are completely indifferent over all possible outcomes. This result is contrasted with the more restrictive implementation findings with either (unrefined) Nash equilibrium or subgame perfect equilibrium.