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 e volutionary game theory succeed to explain the condition for these soc ial interaction to appear, based on the dynamics of different behavior s in the population. The critical importance of the spatial structure as been revealed- if players interact locally, the society to evolve i s very different from if they interact randomly over the whole populat ion. 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 compu ter simulations. Here we apply various mathematical analyses, includin g birth-and-death processes, pair-approximation, and the pair-edge met hod.