Symmetric Stability in Symmetric Games

Abstract

The idea of symmetric stability of symmetric equilibria is introduced which is relevant, e.g., for the comparative-statics of symmetric equilibria with symmetric shocks. I show that symmetric stability can be expressed in a two-player reduced-form version of the N -player game, derive an elementary relation between symmetric stability and the existence of exactly one symmetric equilibrium, and apply symmetric stability to a two-dimensional N -player contest.