Nash implementation via simple stochastic mechanisms: strategy space reduction

Benoît and Ok (Games Econ Behav 64:51–67, <CitationRef CitationID="CR1">2008</CitationRef>) show that in a society with at least three agents any weakly unanimous social choice correspondence (SCC) is Maskin’s monotonic if and only if it is Nash-implementable via a simple stochastic mechanism (Benoît-Ok’s Theorem). This paper fully identifies the class of weakly unanimous SCCs that are Nash-implementable via a simple stochastic mechanism endowed with Saijo’s message space specification (Saijo in Econometrica 56:693–700, <CitationRef CitationID="CR8">1988</CitationRef>). It is shown that this class of SCCs is equivalent to the class of SCCs that are Nash-implementable via Benoît-Ok’s Theorem. Copyright The Author(s) 2012