Effects of Spatial Structures on Evolution of Iterated Prisoner´s Dilemma Game Strategies in Single-Dimensional and Two-Dimensional Grids

We examine the effect of spatial structures on the evolution of iterated prisoner´s dilemma (IPD) game strategies through computational experiments in single-dimensional and two-dimensional grid-worlds. Our computational experiments have two characteristic features. One is the use of a random pairing scheme in the IPD game where each player plays against a different randomly chosen opponent at every round of the dilemma game. The random pairing scheme makes it very difficult for players to evolve cooperative behavior. The other characteristic feature is the use of two neighborhood structures, which follows 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. It is shown that cooperative behavior is evolved only when the interaction neighborhood is very small and the mating neighborhood is small.