Equilibrium Selection Via Stochastic Evolution in Continuum Potential Games

Abstract

We consider stochastic evolution in large population potential games with a continuous strategy set. Examples include aggregative potential games and doubly symmetric games. We approximate the continuous strategy game with a finite strategy game. We then define a stochastic process based on a noisy exponential strategy revision protocol in the finite strategy game. Existing results imply the existence of a stationary distribution of the process on the finite strategy game. We then characterize this stationary distribution as the number of strategies go to infinity and the noise level goes to zero. The resulting distribution puts all its mass on the Nash equilibrium that globally maximizes the potential function of the continuous strategy game. This provides us with an exact history--independent equilibrium selection result in our large population potential game with a continuum of strategies.

Keywords: Potential games, Stochastic evolution, Equilibrium selection.