Equilibria in symmetric games: Theory and applications

This article presents a new approach to analyze the equilibrium set of symmetric, differentiable games by separating multiple symmetric equilibria and asymmetric equilibria. This separation allows the investigation of, for example, how various parameter constellations affect the scope for multiple symmetric or asymmetric equilibria, or how the equilibrium set depends on the nature of the strategies. The approach is particularly helpful in applications because (i) it allows the complexity of the uniqueness problem to be reduced to a two-player game, (ii) boundary conditions are less critical compared to standard procedures, and (iii) best replies need not be everywhere differentiable. The usefulness of the separation approach is illustrated with several examples, including an application to asymmetric games and to a two-dimensional price-information game.