Evolutionary Game Dynamics Based On Complex Networks

In this thesis, we mainly study how network properties and parameters of game models affect the evolutionary game dynamics. In chapter 1, we will firstly give a brief review on the evolutionary game theory, network models and the present research progresses of evolutionary game dynamics on complex networks. In chapter 2, we will focus on studying the dynamics of snowdrift game with memory on complex networks by Monte-Carlo simulations and by mean field theory. Numerical results and theoretical results are in good agreement. In the last chapter, we will summarize the results of our investigations.Recently, the evolutionary game dynamics on complex networks are being widely studied. More realistic game models and game rules are proposed. Wang etc. considered that individuals usually make decisions basing on the knowledge of past records. Thus, they introduced a snowdrift game model with memory. This game model can well capture some factors of realistic game. Basing on the work of Wang, We studied extensively the evolutionary dynamics of the snowdrift game with memory on different networks such as regular network, WS small-world network and BA scale-free network. We mainly focus on how the payoff parameter, memory length, average degree and rewiring probability of WS small-world network affect the frequency of cooperation and the final steady strategy pattern. The main results are: (i) The cooperation frequency varies greatly when the network structure changes from regular network to WS small world network. The result shows that, for r < 0.5, the more regular network is, the more beneficial to cooperation; for r > 0.5, the more random network is, the more beneficial to cooperation. (ii) We find that the frequency of cooperation is not a monotone function of average degree. When the average degree of networks exceeds a certain value, the frequency of cooperation can be significantly increased with the increasing of memory length within a certain range. (iii) We calculate the frequency of cooperation using mean-field theory on networks with different average degree. Theoretical results are in good agreement with numerical results.