Nash implementation via mechanisms that allow for abstentions

Abstract

In this paper, we consider Nash implementability in general settings under the assumption that one may abstain. We show that in the case of at least two individuals, any social choice rule is Nash implementable by mechanisms with abstentions if and only if it is Nash implementable. Moreover, we introduce the notions of minimal participation and participation in equilibrium. We then study the possibility of Nash implementability by mechanisms that satisfy minimal participation or participation.