Neighborhood Specification for Game Strategy Evolution in a Spatial Iterated Prisoner’s Dilemma Game

Abstract

The prisoner’s dilemma is a two-player non-zero-sum game. Its iterated version has been frequently used to examine game strategy evolution in the literature. In this paper, we discuss the setting of neighborhood structures in its spatial iterated version. The main characteristic feature of our spatial iterated prisoner’s dilemma game model is that each cell has a different scheme to represent game strategies. In our computational experiments, one of four representation schemes is randomly assigned to each cell in a two-dimensional grid-world. An agent at each cell has a game strategy encoded by the assigned representation scheme. In this situation, an agent may have no neighbors with the same representation scheme as the agent’s scheme. The existence of such an agent has a negative effect on the evolution of cooperative behavior. This is because strategies with different representation schemes cannot be recombined. When no neighbors have the same representation scheme as the agent’s scheme, no recombination can be used for generating a new strategy for the agent. In our former study, we used a larger neighborhood structure for such an agent. As a result, each agent has a different neighborhood structure and a different number of neighbors. This makes it difficult to discuss the effect of the neighborhood size on the evolution of cooperative behavior. In this paper, we propose the use of the following setting: Each agent has the same number of neighbors with the same representation scheme as the agent’s scheme. This means that each agent has the same number of qualified neighbors as its mates. We also examine a different spatial model where the location of each agent is randomly specified as a point in a two-dimensional continuous space instead of a grid-world.