The geometrical pattern of the evolution of cooperation in the Spatial Prisoner's Dilemma: an intra-group model

Abstract

The Prisoner's Dilemma (PD) deals with the cooperation/defection conflict between two agents. The agents are represented by a cell of $L \times L$ square lattice. The agents are initially randomly distributed according to a certain proportion $ρ_c(0)$ of cooperators. Each agent does not have memory of previous behaviors and plays the PD with eight nearest neighbors and then copies the behavior of who had the greatest payoff for next generation. This system shows that, when the conflict is established, cooperation among agents may emerge even for reasonably high defection temptation values. Contrary to previous studies, which treat mean inter-group interaction, here a model where the agents are not allowed to self-interact, representing intra-group interaction, is proposed. This leads to short time and asymptotic behaviors similar to the one found when self-interaction is considered. Nevertheless, the intermediate behavior is different, with no possible data collapse since oscillations are present. Also, the fluctuations are much smaller in the intra-group model. The geometrical configurations of cooperative clusters are distinct and explain the $ρ_c(t)$ differences between inter and intra-group models. The boundary conditions do not affect the results.