The spread of cooperative strategies on grids with random asynchronous updating

Abstract

The Prisoner’s Dilemma Process on a graph is an iterative process where each vertex, with a fixed strategy (cooperate or defect), plays the game with each of its neighbours. At the end of a round each vertex may change its strategy to that of its neighbour with the highest pay-off. Here we study the spread of cooperative and selfish behaviours on a toroidal grid, where each vertex is initially a cooperator with probability p. When vertices are permitted to change their strategies via a randomized asynchronous update scheme, we find that for some values of p the limiting ratio of cooperators may be modelled as a polynomial in p. Theoretical bounds for this ratio are confirmed via simulation.