Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, and Hierarchical Multi-scale Models

SPATIAL EVOLUTIONARY GAME THEORY: DETERMINISTIC APPROXIMATIONS, DECOMPOSITIONS, AND HIERARCHICAL MULTI-SCALE MODELS SEPTEMBER 2011 SUNGHA HWANG, B.A., SEOUL NATIONAL UNIVERSITY M.A., SEOUL NATIONAL UNIVERSITY Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Luc Rey-Bellet Evolutionary game theory has recently emerged as a key paradigm in various behavioral science disciplines. In particular it provides powerful tools and a conceptual framework for the analysis of the time evolution of strategic interdependence among players and its consequences, especially when the players are spatially distributed and linked in a complex social network. We develop various evolutionary game models, analyze these models using appropriate techniques, and study their applications to complex phenomena. In the second chapter, we derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. These generalize the known mean-field ordinary differential equations and provide powerful tools to