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Pareto-undominated and socially-maximal equilibria in non-atomic games |
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| Affiliation: | 1. International Business School Suzhou, Xi’an Jiaotong-Liverpool University, Jiangsu 215123, China;2. Department of Economics, Ryerson University, Toronto, Ontario M5B 2K3, Canada;1. Department of Economics and Management, University of Pisa, Italy;2. CNRS, CMAP - Ecole Polytechnique, France;1. Paris School of Economics - University Paris 1, CES, 106 bd de l’Hopital, 75013, Paris, France;2. MIA, University of La Rochelle, Avenue Michel Crepeau, 47042, La Rochelle, France;3. University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands |
| Abstract: | This paper makes the observation that a finite Bayesian game with diffused and disparate private information can be conceived of as a large game with a non-atomic continuum of players. By using this observation as its methodological point of departure, it shows that (i) a Bayes–Nash equilibrium (BNE) exists in a finite Bayesian game with private information if and only if a Nash equilibrium exists in the induced large game, and (ii) both Pareto-undominated and socially-maximal BNE exist in finite Bayesian games with private information. In particular, it shows these results to be a direct consequence of results for a version of a large game re-modeled for situations where different players may have different action sets. |
| Keywords: | Non-atomic games Saturated probability space Nash equilibrium Bayes–Nash equilibrium (BNE) Pareto-undominated equilibrium Socially-maximal equilibrium |
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