Evolutionary prisoner's dilemma game on a square lattice

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate (C) or to defect (D) unconditionally. The prayers 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 c-->0 and 1 we have observed critical transitions belonging to the universality class of directed percolation.