Evolutionary prisoner’s dilemma game on a square lattice

Abstract

A simplified prisoner’s game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $\mathrm{}\left(C\right)\mathrm{}$ or to defect $\mathrm{}\left(D\right)\mathrm{}$ unconditionally. The players updated in 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 states when varying the value of temptation to defect. In the limits $\overrightarrow{c}0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.