Symmetry in n-player games

This paper regards symmetry in games with more than two players. It is often said that a two-player game is symmetric if it looks the same to both players. However, there are n-player games, such as Salop's circle model, that seem intuitively to look the same to all players, but do not meet the common definition of a symmetric n-player game. This paper proposes a more general symmetry condition that is satisfied by such models. Previous authors have established that games which are symmetric in the common sense have a number of useful properties relating to equilibrium characterization and comparative statics. With few exceptions, those properties continue to hold in the richer class of games that meet the symmetry condition proposed here.