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Three Notes on Symmetric Games with Asymmetric Equilibria
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It is often the case in symmetric games in normal form that the only existing pure-strategy equilibria are asymmetric. If there is an asymmetric equilibrium for a model with N 'equal" players, then there are multiple equilibria, only differing on the "name" of the players 'assigned" to each one of the actions which together form an equilibrium. A natural question to ask Is, then, how to select among these equilibria. In this note, we show that in symmetric games with a large number of players, an asymmetric pure-strategy equilibrium can be thought of as the approximate outcome of the play of a specific symmetric mixed-strategy equilibrium.
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Cabral, Luis M. B., Three Notes on Symmetric Games with Asymmetric Equilibria (November, 1987). FEUNL Working Paper Series No. 75