Evolutionary prisoner's dilemma game on a square lattice

TL;DR

This paper investigates the evolution of cooperation in a simplified prisoner's dilemma game on a square lattice, analyzing how local interactions and strategy updates influence the emergence of cooperative behavior.

Contribution

It introduces a model combining lattice interactions with probabilistic strategy updates, revealing phase transitions and universality classes in cooperation dynamics.

Findings

Identifies a continuous phase transition between all-defect and all-cooperate states.

Shows the system belongs to the directed percolation universality class.

Demonstrates critical behavior at the transition points.

Abstract

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing state when varying the value of temptation to defect. In the limits $c \to 0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.