Abstract
Benoît and Ok (2008) 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, 1988). It is shown that this class of SCCs is equivalent to the class of SCCs that are Nash-implementable via Benoît-Ok's Theorem.