Selection intensity and risk-dominant strategy: A two-strategy stochastic evolutionary game dynamics in finite population

Stochastic evolutionary game dynamics with weak selection in finite population has been studied and it has been used to explain the emergence of cooperation. In this paper, following the previous studies, the diffusion approximation of a two-strategy stochastic evolutionary game dynamics in finite population that includes a small mutation rate between two strategies is investigated, where we assume that these two strategies are both strict Nash equilibrium (NE). Our main goal is to partially reveal the effect of selection intensity on the stochastic evolutionary game dynamics. Through the analysis of potential function of the stationary distribution, our main result shows that for all possible situations with that the selection intensity is not zero (that includes the strong selection), if a strategy is a risk-dominant NE, then its expected fitness with respect to the stationary distribution must be larger than that of other strategy. This result not only extends the previous results but also provides some useful insights for understanding the significance of selection intensity in stochastic evolutionary game dynamics in finite population.