  Animal behavior and evolution can often be described by game-theoretic
models. Although in many situations, the number of players is very large, their
strategic interactions are usually decomposed into a sum of two-player games.
Only recently evolutionarily stable strategies were defined for multi-player
games and their properties analyzed (Broom et al., 1997). Here we study the
long-run behavior of stochastic dynamics of populations of randomly matched
individuals playing symmetric three-player games. We analyze stochastic
stability of equilibria in games with multiple evolutionarily stable
strategies. We also show that in some games, a population may not evolve in the
long run to an evolutionarily stable equilibrium.
