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.