The long-run behavior of interacting individuals can be often described within 
game-theoretic models. We discuss a stochastic adaptation dynamics of a finite 
population of players. We analyze two-player games with two evolutionarily stable 
strategies: an efficient one which provides maximal payoffs and a risk-dominant one 
played by individuals averse to risk. We address the problem of equilibrium selection 
- which strategy is played in the long run with a high frequency. 
    Our results show that when the number of players increases, the population undergoes 
twice a transition between its equilibria. Therefore, to describe the long-run behavior
in any specific model, one has to evaluate the number of players and the mutation level. 

References

1. J. Miękisz, Equilibrium selection in evolutionary games with random matching of players, 
   J. Theor. Biol. 232: 47-53 (2005).

2. D. Kamiński, J. Miękisz, and M.Zaborowski, Stochastic stability in three-player games, 
   Bull. Math. Biol. 67: 1195-1205 (2005).
 
All recent papers can be downloaded from www.mimuw.edu.pl/~miekisz