Phase transition in evolutionary games

The evolution of cooperative behavior is studied in the deterministic versi on of the Prisoners' Dilemma on a two-dimensional lattice. The payoff param eter is set at the critical region 1.8 < b < 2.0, where clusters of coopera tors are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the dis tribution of cooperators is studied as a function of the bin size covering varying numbers of lattice cells. From the scaling behavior of the moments a scaling exponent is determined and is found to lie in the range where pha se transitions are known to take place in physical systems. It is therefore inferred that when the payoff parameter is increased through the critical region the biological system of cooperators undergoes a phase transition to defectors. The universality of the critical behavior is thus extended to i nclude also this particular model of evolution dynamics.