Study Of Complex Networks And Evolutionary Game Dynamics On Networks

Complex network is a new branch of science that studies complex systems, which has attracted much attention from scientific researchers. Any complex systems in nature are composed of many intereacting units, such as the Internet, World Wide Web, airport networks, power grids, protein-protein interaction networks and collaboration networks, etc. These networks are of high technological and intellectual importance and the desire to understand such complex systems has encountered significant chanllenges as well. Inspired by the current international research interests, we investigate the structural properties of the hybrid evolving and inner evolving networks, address how the evolution of cooperation is affected by the network topology, and explore some possible mechanisms supporting the emergence and maintance of cooperation based on the commonly-used game models.The main work and contributions are as follows:1,A hybrid evolving network model is proposed. When a node enters into the network, the glocal or local preferential attachment is carried out with a certain probability. Both theoretical analysis and numerical simulations show that the degree distributions of the generated networks can vary from power-law distribution to exponential distribution by adjusting the model parameter. Furthermore, the model reduces the fragility against intentional attacks while preserving the robustness against random failures.2,An inner evolving network model is proposed. Based on the extended rate equation approach, we analyze theoretically the degree distribution and joint degree distribution and perform corresponding numerical simulations. It is found that the theoretical analysis is in good agreement with the numerical results. When the preferential attachment is linear, the degree distributions follow the power-law form. For the sub-linear preferential selecition, the degree distributions follow the form of stretched exponential. For the sup-linear preferential attachment, the double endpoint preferential attachment can lead to an extremely low number of"gel"nodes that connect to nearly every other node in the network. The nontrivial degree correlation and joint degree distribution are established during the growing process.3,We explore the prisoner's dilemma game on two types of positively correlated networks. Evolution is carried out by implementing the finite population analogue of replicator dynamics. It is found that the networks with positive degree correlation can either promote or inhibit the emergence of cooperation. Furthermore, we investigate the probability to cooperate as a function of the node connectivity, and find that high-degree individuals overall have a higher probability to cooperate. It is also found that small-degree individuals usually change their strategies more frequently, and such change is shown to be unfavorable to cooperation.4,We investigate the prisoner's dilemma game on Newman highly clustered community networks with tunable clustering coefficients and community sizes. Evolution is carried out by implementing the finite population analogue of replicator dynamics. It is found that the clustering coefficient in such a degree-homogeneous network inhibits the emergence of cooperation for the entire range of the payoff parameter. It is also found that community size can also have a marked influence on the evolution of cooperation, with a larger community size leading to not only the lower cooperation level but also the smaller threshold of the payoff parameter above which cooperators become extinct.5,We investigate the evolutionary prisoner's dilemma game and the snowdrift game on Newman-Watts small-world networks with local contribution and introspection. In the games, individuals not only concentrate on their own incomes but also consider the local contributions to their neighbors. Furthermore, individuals have the ability of self-questioning and the strategy updating is determined by the comparison between the payoffs obtained with cooperation and defection, i.e., after each real round of games, each player plays a virtual round of games and then adopts the strategy leading to a higher payoff. Studies show that cooperation emerges easily in the population in this model.6,We investigate the prisoner's dilemma game and snowdrift game on community networks with active linking dynamics. In the game, individuals can break old links and establish new links with their neighbors. We assume that individuals in the same community have a higher probability to establish links than individuals belonging to different communities. We carry out both theoretical analysis and numerical simulations, finding good agreement with each other. Studies show that community structure is more favorable to cooperation. The results are robust with respect to both the initial number of cooperators and the time-scale ratio of linking dynamics to strategy updating dynamics.7,In order to understand the memory effects in the evolutionary game dynamics, a memory-based prisoner's dilemma game model is proposed and analyzed. It is assumed that individuals update their strategies according to the accumulative payoffs in the past several time steps. When updating strategies, individuals imitate the behavioral patterns of their neighbors, i.e., they cooperate or defect with the same probability as their neighbors. Studies show that cooperation can be greatly enhanced. We have checked that the current mechanism which promotes cooperation is robust with respect to both the ways of streategy updating and neighbor selection.8,We study the payoff-accumulative effect on the evolution of cooperation in the prisoner's dilemma game. In our model, the payoff in effect is the accumulative payoff from the very beginning of the evolutionary process, but the strategy imitated by individuals is the strategy in the current time step. It is found that when individuals focus on the accumulative payoff, cooperators are favorable by selection. It is a universal rule that can promote cooperation, which is robust with respect to the way of strategy updating and the underlying interaction network.9,We investigate the prisoner's dilemma game on square lattices based on the average payoff. In the model, each individual updates its strategy by learning all neighbors in the neighborhood instead of by learning from a single neighbor. After each round of game, each individual separates all their neighbors into two groups: cooperative group and defecting group, and then adopts the strategy of the individuals in the group with a higher average payoff. Studies show that cooperation can be effectively promoted by such an updating rule, which is caused by the fact that cooperators can help each other in a wider range.