  We discuss the long-run behavior of stochastic dynamics of many interacting
players in spatial evolutionary games. In particular, we investigate the effect
of the number of players and the noise level on the stochastic stability of
Nash equilibria. We discuss similarities and differences between systems of
interacting players maximizing their individual payoffs and particles
minimizing their interaction energy. We use concepts and techniques of
statistical mechanics to study game-theoretic models. In order to obtain
results in the case of the so-called potential games, we analyze the
thermodynamic limit of the appropriate models of interacting particles.
