Three Notes on Symmetric Games with Asymmetric Equilibria

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.N/