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A cellular automaton in which cells represent agents playing the Prisoner'sDilemma (PD) game following the simple "win-stay, loose-shift" strategy isstudied. Individuals with binary behavior, such as they can either cooperate(C) or defect (D), play repeatedly with their neighbors (Von Neumann's andMoore's neighborhoods). Their utilities in each round of the game are given bya rescaled payoff matrix described by a single parameter Tau, which measuresthe ratio of 'temptation to defect' to 'reward for cooperation'. Depending onthe region of the parameter space Tau, the system self-organizes - after atransient - into dynamical equilibrium states characterized by differentdefinite fractions of C agents (2 states for the Von Neumann neighborhood and 4for Moore neighborhood). For some ranges of Tau the cluster size distributions,the power spectrums P(f) and the perimeter-area curves follow power-lawscalings. Percolation below threshold is also found for D agent clusters. Wealso analyze the asynchronous dynamics version of this model and compareresults.Comment: Accepted for publication in JSTA

Spatial patterns and scale freedom in Prisoner’s Dilemma cellular automata with Pavlovian strategies