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Full-Text Articles in Physical Sciences and Mathematics
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, And Hierarchical Multi-Scale Models, Sung-Ha Hwang
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, And Hierarchical Multi-Scale Models, Sung-Ha Hwang
Open Access Dissertations
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 …
Decompositions Of Two Player Games: Potential, Zero-Sum, And Stable Games, Sung-Ha Hwang, Luc Rey-Bellet
Decompositions Of Two Player Games: Potential, Zero-Sum, And Stable Games, Sung-Ha Hwang, Luc Rey-Bellet
Luc Rey-Bellet
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal complements which we call anti-potential games and anti-zero-sum games, respectively. Perhaps surprisingly, every anti-potential game comes either from the Rock-Paper-Scissors type games (in the case of symmetric games) or from the Matching Pennies type games (in the case of asymmetric games). Using these decompositions, we prove old (and some new) cycle criteria for potential and zero-sum games (as orthogonality relations between subspaces). …