Self-organized Criticality In Spatial Evolutionary Games

The emergence of cooperation is a fundamental problem in the theory of evolution because unselfish, altruistic actions apprently contradict Darwinian selection. Another question is why evolution exhibits “punctuated equilibrium”phenomenons, which are the characteristics of dynamical systems in a critical state. In this thesis, we begin with a brief introduction to spatial evolutionary games and some models about self-organized criticality and then we try to discuss the above two puzzles simultaneously base on the generalized Bak-Sneppen(BS)model.BS model characteristics the evolution of biological systems in a simple way,which can naturally evolve to a critical state. We study an iterated Snowdrift Game and a Prisoners’ Dilemma Game on different network structures, however, for the competitive mechanism between agents we introduce the Bak-Sneppen(BS) evolution model. Initially, each agent is assigned to a random cooperation probability and its fitness is given by the payoffs from neighbors. At each time step, the agent with minimun fitness and its neighbors will change their cooperation probability. We show the evolution of the cooperation probabilities of the least fit members and their neighbors and the mean cooperation probability and then analyse the reason why cooperation is promoted. Besides, we measure the distribution of avalanche size and the distance between successive minimum fitness sites by connecting BS model with two game models, which are well fit by a power law approximately. The power law we measured shows that the system has reached a critical state. In the critical state the agents are connected at all scales which closely connected with the high level cooperation in the system.