Evolutionary Games And Statistical Behavior On Complex Networks

The real world is constructed with many complex systems. From the point view of topology, these systems may be abstracted as the complex networks. Nowadays, complex networks are important mathematical tools to study and explore the structure and function of different complex systems in nature and society. After the publication of two classic documents, titled as"Collective Dynamics of'Small-World'Networks"and"Emergence of Scaling in Random Networks", a series of research works about complex networks such as different structures of topology, the function of networks and evolutionary rules have been published by scientists from different studying fields. In this thesis, we will focus on evolutionary dynamics of different games on networks including the evolutionary properties and statistical behavior. Our main work is listed below.Firstly, we study the snowdrift game on networks under different evolutionary rules. The evolutionary rules include imitation mechanism and self-questioning mechanism. Our results show that the cooperation frequency of the system has different features under the different evolutionary rules. Under the imitation mechanism, we find the system can obtain higher payoff on average. This feature is of benefit to the whole competing system, which is based on sucking the labor value of the cooperators.Secondly, we study the statistical features that animal conflict evolves on different networks. Maynard and Price presented the logic of animal conflict. In their model, they presented five possible strategies that the animals may use when they have a contest. Their results indicated that animals usually use the limit-war strategy, which does not cause a serious injury during the conflicts. The strategy of retaliator and the strategy of prober-retaliator are both the evolutionary stable strategies. If the relation between animals has a complex network structure, the evolutionary strategies may have a different result from that of Maynard's. On some networks, we find that only one strategy can survive, and on other networks, two certain strategies can survive together, or even more strategies may coexist. These results show that the structure of networks have great effects on the final survival strategies among conflicts.Thirdly, we combine the snowdrift game and the evolutionary rules of minority game to study the cooperative behavior in multi-agents competing system. With different cost-to-reward ratios, both the minority (the number of cooperators less than the half of the population) and the majority of cooperators can be the winners. We find that the cooperation frequency shows the plateau structure when it is as a function of the cost-to-reward ratios. Furthermore we also study the standard deviation of cooperation frequency varies as functions of the cost-to-reward ratios and memory length. We find that the cost-to-reward ratios and memory length affect significantly the efficiency of competitors for competing the available winning quota.