Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation

Contributions by E. Maskin and S. Williams have established that any social choice cor respondence satisfying monotonicity, no veto power, and having at lea st three participants is Nash implementable under the proviso that th e number of social alternatives is finite and that the correspondence satisfies citizen sovereignty. The author makes improvements in two aspects of their Nash implementation theorems: a reduction in the str ategy space and a proof for an arbitrary alternative set. Each partic ipant announces two participants' preferences, an alternative, and a positive integer. With this strategy space specification, the author confirms Maskin's theorem for an arbitrary size of the alternative se t.