The evolution of social interaction in lattice models

The rationality of human behavior seems unable to explain the altruism and spite which gives the player a short-term cost. Recent study of evolutionary game theory succeed to explain the condition for these social interaction to appear, based on the dynamics of different behaviors in the population. The critical importance of the spatial structure as been revealed - if players interact locally, the society to evolve is very different from if they interact randomly over the whole population. In this article, we review the studies on the evolution of social interaction in lattice structured models (or cellular automata models). The analysis of lattice models have been restricted to direct computer simulations. Here we apply various mathematical analyses, including birth-and-death processes, pair-approximation, and the pair-edge method.