On a continuous mixed strategies model for evolutionary game theory

TL;DR

This paper introduces an integro-differential model for evolutionary game theory that analyzes the evolution and stability of mixed strategies, providing analytical insights and numerical schemes for multiple strategies.

Contribution

It presents a reformulation based on first moments, analyzes asymptotic behavior and stability for two strategies, and proposes numerical schemes for capturing equilibrium states.

Findings

Analytical properties and global estimates of the model

Asymptotic behavior and stability for two strategies

Numerical schemes effectively capture equilibrium states

Abstract

We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical properties of the model and global estimates. The asymptotic behavior and the stability of solutions in the case of two strategies is analyzed in details. Numerical schemes for two and three strategies which are able to capture the correct equilibrium states are also proposed together with several numerical examples.