A Full Characterization of Nash Implementation with Strategy Space Reduction

Noting that a full characterization of Nash-implementation is given using a canonical-mechanism and Maskin's theorem (Maskin, 1999) is shown using a mechanism with Saijo's type of strategy space reduction (Saijo, 1988), this paper fully characterizes the class of Nash-implementable social choice correspondences (SCCs) by mechanisms endowed with Saijo's message space specification - s-mechanisms. This class of SCCs is equivalent to the class of Nash-implementable SCCs, though any further `strategy space reduction' mechanism breaks this equivalent relationship down