  We discuss similarities and differencies between systems of many interacting
players maximizing their individual payoffs and particles minimizing their
interaction energy. We analyze long-run behavior of stochastic dynamics of many
interacting agents in spatial and adaptive population games. We review results
concerning the effect of the number of players and the noise level on the
stochastic stability of Nash equilibria. In particular, we present examples of
games in which when the number of players or the noise level increases, a
population undergoes a transition between its equilibria.
