The women of Cairo: Equilibria in large anonymous games |
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| Institution: | 1. School of Informatics, University of Edinburgh, EH8 9AB, United Kingdom;2. College of Information System and Management, NUDT, Changsha 410073, China;1. Université Paris 1, 106-112, Bd de l’Hôpital, 75013 Paris, France;2. Université de Lyon, Lyon, F-69007, France;3. CNRS, GATE Lyon Saint-Etienne, Ecully, F-69130, France;4. University Jean Monnet, Saint-Etienne, F-42000, France;5. Paris School of Economics, Université Paris 1, 106-112, Bd de l’Hôpital, 75013 Paris, France |
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| Abstract: | In this article, I characterize Nash equilibria of large anonymous games by providing the following neccessary and sufficient condition for an equilibrium distribution: for no subset K of actions more players play actions in K than have a best response in K to the given distribution. While neccessity is trivial the proof for sufficiency relies on a theorem by Math. Proc. Camb. Philos. Soc. 78 (1974) 323] which is an extension of Hall’s theorem or the marriage lemma well known from graph theory. The veiling problem for the women of Cairo serves as an illustrating heuristic example explaining the nature of the result. |
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