Research On The Movement And Convergence Of Evolutionary Game In Complex Networks

Game theory researches on strategies of related individuals with benefit. In the interactions, the benefit of individuals not only base on their strategies, but also rely on strategies of others. Evolutionary game theory focuses its attention on how bounded rationality individuals get maximal payoff with adaptive study during repeated game process. As one of branches in the field of applied mathematics, game theory has been widely applied in biological, economic, political, information and many other subjects.Complex network theory provides a convenient framework to describe the game relations between individuals. Nodes in network indicate individuals and sites stand for interactions between individuals. In this way, we can use the complex network topology to study the relations of the game on this network.The dissertation surveys a wide range of related works and current situation of evolutionary game dynamics on complex networks, and discusses influence of long-distance moving in spatial lattice network, adaptive distribution according to the individuals strategy on periodic boundary plane, and the relation between the largest Laplacian eigenvalue of the network and the critical value of benefit-to-cost ratio of snowdrift game.The main contributions of this dissertation are summarized as follows:1. We research how moving distance effect the game behaviors in two dimension spatial lattice network. We find that moving distance bring different result. Short distance moving promotes emergence of cooperation behavior, but long distance moving let defectors can get benefit from cooperators more easily, which inhibit cooperation behavior. We explain the reason by sorting the moving distance of individuals.2. We use strategies of individuals to determine the adaptive distribution in two dimension plane. Basing on model of Helbing and Hanxin Yang, we observe the distribution of pure strategy individuals. We find the cooperation behavior emergence by introducing a cooperator in population of defectors. The probability of cooperation can stabilize at one level and strategies can coexist.3. We consider the relation between the largest Laplacian eigenvalue of the network and the critical value of benefit-to-cost ratio of snowdrift game. When it meets a certain relations, individuals strategy can appear convergence. We also find that the theoretical calculation and practical simulation results are very anastomotic.