Spatialized Evolutionary prisoner's dilemma: Homogenization and propagation of chaos

TL;DR

This paper rigorously analyzes a spatial evolutionary prisoner's dilemma model, demonstrating its convergence to a mean field model through homogenization and propagation of chaos, thus providing a theoretical foundation for observed cooperative behavior.

Contribution

It introduces a particle system framework to prove the convergence of a spatial evolutionary game to a mean field model, advancing theoretical understanding.

Findings

Convergence of the spatial model to a random matching model

Convergence of the random matching model to a mean field model

Theoretical validation of cooperation persistence in spatial games

Abstract

Epstein introduced an agent-based model called Demographic Prisoner's dilemma. He shows, via simulations, that cooperation in this spatial evolutionary repeated game can be sustained. In order to do proves, we put on this model a particle system framework in order to prove the convergence of the spatial model to a random matching model, using homogenization techniques. Then we prove the convergence of the random matching model to a mean field model, using propagation of chaos techniques.