Nash implementation via simple stochastic mechanisms: strategy space reduction |
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Authors: | Michele Lombardi |
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Institution: | 1. Department of Quantitative Economics, Maastricht University, P. O. Box 616, 6200 MD, Maastricht, The Netherlands 2. Department of Economics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
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Abstract: | Beno?t 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 (Beno?t-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 Beno?t-Ok’s Theorem. |
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