Roles of Space and Geometry in the Spatial Prisoners’ Dilemma

The spatial prisoners’ dilemma is a useful model in stochastic game theory that can help probe spatial complexity classes and quantify macroscopic emergent properties. Repeated simulation experiments with different temptation payo↵ parameter values and with varying initial proportions of defector players indicate a detailed structure in phase space that exhibits sharp transitions regardless of the spatial dimension and grid geometry employed. These edges appear to be a complex but natural consequence of the spatial prisoners’ dilemma and similar models. Applying a damping or self-weight to the choice of game strategy employed also shifts the edges in parameter space. This article presents detailed results from numerical experiments on the spatial prisoner dilemma model and discusses implications for other stochastic spatial game theory agent systems.