Nash implementation via hyperfunctions

Hyperfunctions are social choice rules which assign sets of alternatives to preference profiles over sets. So, they are more general objects compared to standard (social choice) correspondences. Thus every correspondence can be expressed in terms of an equivalent hyperfunction. We postulate the equivalence between implementing a correspondence and its equivalent hyperfunction. We give a partial charaterization of Nash implementable hyperfunctions and explore the conditions under which correspondences have Nash implementable equivalent hyperfunctions. Depending on the axioms used to extend preferences over alternatives to sets, these conditions are weaker than or logically independent of Maskin monotonicity, in any case expanding the set of Nash implementable social choice rules. In fact, social choice rules such as the majority rule and the top cycle are Nash implementable through their equivalent hyperfunctions while they are not Maskin monotonic, thus not Nash implementable in the standard framework. * İstanbul Bilgi University, Department of Economics, İnonu Cad. No.28, İstanbul, 80310, Turkey; corresponding author, [email protected] ** İstanbul Bilgi University, Department of Economics, İnonu Cad. No.28, İstanbul, 80310, Turkey.