Abstract

The authors investigate the implementation of social choice functions that map to lotteries over alternatives. They require virtual implementation in iteratively undominated strategies. Under very weak domain restrictions, they show that if there are three or more players, any social choice function may be so implemented. The literature on implementation in Nash equilibrium and its refinements is compromised by its reliance on game forms with unnatural features (for example, integer games) or modulo constructions with mixed strategies arbitrarily excluded. In contrast, the authors' results employ finite (consequently well-behaved) mechanisms and allow for mixed strategies.

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