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

A cellular automaton in which cells represent agents playing the Prisoner's Dilemma (PD) game following the simple 'win—stay, lose—shift' strategy is studied. Individuals with binary behaviour, such that they can either cooperate (C) or defect (D), play repeatedly with their neighbours (Von Neumann's and Moore's neighbourhoods). Their utilities in each round of the game are given by a rescaled pay-off matrix described by a single parameter τ, which measures the ratio of temptation to defect to reward for cooperation. Depending on the region of the parameter space τ, the system self-organizes—after a transient—into dynamical equilibrium states characterized by different definite fractions of C agents (two states for the von Neumann neighbourhood and four for the Moore neighbourhood). For some ranges of τ the cluster size distributions, the power spectra P(f) and the perimeter–area curves follow power law scalings. Percolation below threshold is also found for D agent clusters. We also analyse the asynchronous dynamics version of this model and compare results.

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