General conditions for strategy abundance through a self-referential mechanism under weak selection

We examine stochastic evolutionary game dynamics of two-player m×m symmetric and m×n asymmetric games in finite populations assuming that a player decides to change her current strategy on the basis of her dissatisfaction, which we call a self-referential mechanism. We derive the general expression for the stationary distribution of strategy under weak selection and compare it with the counterpart of a Moran process. As a result, we find that both in symmetric games and in asymmetric games, the self-referential mechanism always generates a greater gap between the favored and unfavored strategies' frequencies for a fixed parameter set than does a Moran process. Further, we found that for small mutation rates, our results are almost identical to the counterpart of a Moran process.