We discuss similarities and differences between systems of interacting players
maximizing their individual payoffs and particles minimizing their interaction energy.
Long-run behavior of stochastic dynamics of spatial games with multiple equilibria
is analyzed. In particular, we construct an example of a spatial game with three
strategies, where stochastic stability of Nash equilibria depends on the number
of players and the kind of dynamics.
Key Words : evolutionary game theory, Nash equilibria,
cellular automata, stochastic stability.