Strategy abundance in 2×22×2 games for arbitrary mutation rates

We study evolutionary game dynamics in a well-mixed populations of finite size, NN. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, AA and BB, under mutation and selection. The game dynamical interaction between the two strategies is given by the 2×22×2 payoff matrix (acbd). It has previously been shown that AA is more abundant than BB, if a(N-2)+bN>cN+d(N-2)a(N-2)+bN>cN+d(N-2). This result has been derived for particular stochastic processes that operate either in the limit of asymptotically small mutation rates or in the limit of weak selection. Here we show that this result holds in fact for a wide class of stochastic birth–death processes for arbitrary mutation rate and for any intensity of selection.