The Phase Structure in the Evolution of Globally coupled Spatial Prisoner's Dilemma

Abstract

We propose two new evolutionary rules that is not mimic evolution of strategies based on the spatial Prisoner's Dilemma (PD). The former follows the selfish evolutionary rule and then the coexistence phase appears with weak phase transition with mutations. The second rule is that of globally coupled spatial PD where the strategy of an agent is taken so that the total payoff of the whole system increases. Then it is natulally suspected that all agents will become cooperators in general. We, however, find that situations is rather complerx. We find two critical points within the usual conditions in the parameters included the payoff matrix in the PD. Further as we break the condition without losing PD condition, we meet two more essential curitical points. We discuss the areas between these critical points in the parameter space and uncover the various properties by simulating on computer. We show that in some parameter regions, strange properties, that is, like chaotic behaveor appear and the coexistence between defectors and cooperators appears in the large parameter region. Thus we point out that usual non-essential condition among the parameters in the payoff matrix imposed on the PD privent from recovering rich structures in the evolutionally spatial PS.