  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.
