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...In that case we say that f is Nash implementable. The following theorem, due to Maskin (1999), shows that monotonicity is an important necessary condition for a SCC to be Nash implementable. Theorem (=-=Maskin, 1999-=-). If a SCC f : D →X is not monotonic, then it is not Nash implementable. Maskin (1999) also proves that, with at least three agents, monotonicity is sufficient for Nash implementation when the ‘No Ve...

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...dy the preference domains on which we can implement Condorcet extensions. It is well known that Condorcet extensions are not Nash implementable when all strict or all weak preferences are admissible (=-=Jackson, 2001-=-; Saijo, 1987, e.g.). Maskin (1999) shows that Condorcet extensions are Nash implementable when only †The authors thank Yaron Azrieli for his helpful comments. ∗Dept. of Economics, The Ohio State Univ...