Abstract
Consider the problem of exact Nash implementation of social choice correspondences. Define a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. We call such a game form a lottery mechanism. When preferences over alternatives are strict, we show that Maskin Monotonicity (Maskin, 1999) is both necessary and sufficient for the Nash implementation of social choice correspondences satisfying unanimity. We discuss how to dispense with unanimity and relax the assumption of strict preferences by modifying the canonical mechanism we consider. We then study some examples of Maskin monotonic social choice correspondences violating no-veto power. Finally, we apply our method to the issue of voluntary implementation (Jackson-Palfrey, 2001).
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