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

TL;DR

This study explores how spatial patterns and scale invariance emerge in a cellular automaton modeling Prisoner's Dilemma with Pavlovian strategies, revealing power-law behaviors and cluster dynamics across different parameters.

Contribution

It introduces a cellular automaton model with Pavlovian strategies for Prisoner's Dilemma, analyzing spatial patterns, scale invariance, and the effects of different neighborhoods and update rules.

Findings

Power-law scaling in cluster size distributions and power spectra.

Different equilibrium fractions of cooperators depending on Tau.

Percolation phenomena observed below threshold.

Abstract

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