Abstract
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.
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References
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Acknowledgments
We are grateful to Hans Peters and Naoki Yoshihara for useful comments and suggestions. Special thanks go to an anonymous referee and an Editor-in-Chief of this journal, whose comments and suggestions have led to substantial improvements in the paper. The usual caveat applies.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Lombardi, M. Nash implementation via simple stochastic mechanisms: strategy space reduction. Rev Econ Design 16, 297–309 (2012). https://doi.org/10.1007/s10058-012-0117-7
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DOI: https://doi.org/10.1007/s10058-012-0117-7