The Evolutionary Games And Dynamics In Complex Networks

Many complex systems in nature could be considered as networks composed of intereacting units, such as biological systems, social systems, economic systems, and so on. On the other hand, the mechanisms of cooperation emerging and maintaining from selfish individuals have attracted more and more interests, while evolutionary game theory provides a unifying framework to address them. In networks, individuals are located on sites and interactions among them are described by edges of networks. Based on these, we can build evolutionary dynamics and research the effects of different network structures and different evolutionary processes on cooperation. These investigations could help us understand the emergence and maintainance of cooperation and furthermore find more mechanisms which might promote cooperation in evolutionary games.In this dissertation, we first introduce some fundamental concepts of complex networks and typical network models, then summary present studies about evolutionary games. Based on these, we investigate several further issues about evolutionary games on complex networks as following.Firstly, we focus on the effects of individuals' degrees on spontaneous cooperation. By investigating evolutionary prisoner's dilemma games (PDGs) on random networks with two distinct degrees, we find some resonance-type behaviors of the cooperator frequency with the variation of degree. We also find that increasing hub's degree actually disfavors the cooperation though the heterogeneity in degree can enhance cooperation in the population.Secondly, we investigate the game theory in a structured population with the assumption that the evolution of network structure is far faster than that of strategy update. We find that the degree distribution for the final network consists of two distinct parts:the low degree part which is contributed by defectors and a broadband in the regime with high degree which is formed by cooperators. The structures of the final network and the final strategy pattern have also been numerically proved to be independent of the game parameters.Thirdly, we introduce a simple model to investigate the crossover between a structured network and a well-mixed one in an evolutionary PDG. In the model, each link j is designated a rewiring parameter?j, which defines the time interval between two successive rewiring events for link j. Through adjusting the rewiring parameter?(the mean time interval for any link in the network), we could change a structured network into a well-mixed one. For the link rewiring events, three situations are considered:one synchronous situation and two asynchronous situations. Simulation results show that there are three regimes of?:large?where the density of cooperators rises to the value for the case without link rewiring, small?where the mean-field description for a well-mixed network is applicable, and moderate?where the crossover between a structured network and a well-mixed one happens.Fourthly, we investigate the effects of double-dealing behavior on cooperation in evolutionary games. Each individual in a population has two attributes:character and action. One's action may be consistent with her character or not. We provide analytical results by a mean-field description of evolutionary PDGs. Moreover, we give numerical results on different networks, ranging from square lattices to scale-free networks (SFNs). Two important conclusions have been drawn from the results on SFNs. Firstly, if only non-influential individuals (those with low degrees) have chances of becoming double-dealers, cooperation is certain to deteriorate. Secondly, when influential individuals (those with high degrees) adopt double-dealing behavior moderately, cooperation would be enhanced. These results help us to understand better the social phenomenon of the existence of double-dealers. In addition to the PDG, other types of games including the snowdrift game, the stag-hunt game and the harmony game have also been studied on our model. The results for these three games are also presented, which are consistent with the results for the PDG qualitatively.