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Nash implementation via simple stochastic mechanisms: strategy space reduction. (English) Zbl 1282.91135
Summary: J.-P. Benoît and E. A. Ok [Games Econ. Behav. 64, No. 1, 51–67 (2008; Zbl 1153.91394)] 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 T. Saijo’s message space specification [Econometrica 56, No. 3, 693–700 (1988; Zbl 0652.90014)]. It is shown that this class of SCCs is equivalent to the class of SCCs that are Nash-implementable via Benoît-Ok’s theorem.

MSC:
91B26 Auctions, bargaining, bidding and selling, and other market models
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