Potential Games with Continuous Player Sets

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition arising naturally in models of network congestion. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to equilibrium from all initial conditions. We propose a subclass of potential games in which evolution leads to efficient play. Finally, we show that the games studied here are the limits of convergent sequences of the finite player potential games studied by Monderer and Shapley (1996). JEL Classification Numbers: C72, C73, D62, R41.