On a continuous mixed strategies model for evolutionary game theory

Abstract

We consider an integro-differential model for evolutionary gametheory which describes the evolution of a population adopting mixed strategies.Using a reformulation based on the first moments of the solution, we provesome analytical properties of the model and global estimates. The asymptoticbehavior and the stability of solutions in the case of two strategies is analyzedin details. Numerical schemes for two and three strategies which are able tocapture the correct equilibrium states are also proposed together with severalnumerical examples. © American Institute of Mathematical Sciences