Effects of spatial structures on evolution of iterated prisoner’s dilemma game strategies with probabilistic decision making

We have examined the effect of spatial structures on the evolution of iterated prisoner´s dilemma (IPD) game strategies. In our former study, we used two neighborhood structures, which follow the concept of structured demes. One is for the interaction among players through the IPD game. A player in each cell in a grid-world plays against its neighbors defined by this neighborhood structure. The other is for the mating of strategies by genetic operations. A new strategy for a player is generated by genetic operations from a pair of parent strings, which are selected from its neighbors defined by the second neighborhood structure. In this paper, we extend our IPD game simulation to a more realistic problem while keeping the simplicity of the original IPD game. We employ a stochastic strategy represented by a string of real numbers between 0 and 1. Each real number in the string denotes the probability of cooperation. We examine the effects of spatial structures on the evolution of IPD game strategies with probabilistic decision making in various payoff matrices. From simulation results, it is shown that cooperative behavior is evolved only when the interaction neighborhood is small and the mating neighborhood is also small for some payoff matrices.