Stochastic evolutionary selection in finite populations

Abstract

We primarily focus on a wide range of stochastic evolutionary game dynamics between two strategies which are characterized by a condition we call monotonicity: the sign of the difference between the probabilities of increasing and decreasing an A-individual completely depends on the difference of payoffs based on different strategies. When mutations are excluded, we provide sufficient conditions for selection to favor one strategy over the other and necessary conditions for selection to favor or oppose change, respectively. Moreover, we discuss which strategy will be favored in case of rare mutations and give a simple rule to determine evolutionary selection of strategies for large populations under some specific stochastic mutation–selection dynamics.