Robustness of equilibria in anonymous local games

This paper studies the robustness of symmetric equilibria in anonymous local games to perturbations of prior beliefs. Two priors are strategically close on a class of games if players receive similar expected payoffs in equilibrium under the priors, for any game in that class. I show that if the structure of payoff interdependencies is sparse in a well-defined sense, the conditions for strategic proximity in anonymous local games are strictly weaker than the conditions for general Bayesian games of Kajii and Morris (1998) [11] when attention is restricted to symmetric equilibria. Hence, by exploiting the properties of anonymous local games, it is possible to obtain stronger robustness results for this class.