Nash implementation via simple stochastic mechanisms : strategy space reduction

Benoît and ok (games econ behav 64:51–67, 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 in econometrica 56:693–700, 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.