Study Of Evolutionary Game Dynamics On Spatial Lattice

The evolutionary game theory roots from the evolution of biology, it is a kind of theory which combines the game theory analysis and the dynamic evolution process analysis, the object we research is a certain group of people as time goes on, the purpose of theoretical exploration is to understand the dynamic process of groups evolution and explain why the groups can achieve this state at present and how to achieve it. People use the nodes on network represent individuals in the game and the edges represent the relations of the individual with its neighbors, the researchers found that the individuals of the game would be drawn into spatial lattice so that the game problem can be got a better solution. In recent years, the evolutionary game on spatial lattice have got wide attention and acquired plentiful of results.In this paper, based on the evolutionary game theory and complex network theory which was used to research the cooperation behavior between the selfish individual, first we probe the impact of the average degree of the network formed by the cooperative behavior of public goods game, second we discuss the memory effect on the spatial public goods game and noise intensity of impact on the evolution of cooperation in detail. Specific content is as follows:(1) The average degree of the network is one of the topological characteristics which has important influence on dynamics of game, we use the Monte-Carlo numerical simulation method to research the impact of network average degree on the public goods game of cooperative behavior and during the process we adopt the one-dimensional rule network model (neighbor coupled network). We found that the effect of average degree of network on the evolution of cooperation depends on the size of the gain coefficient. During the research we use the method of mean field approximation as a theory analysis tool. Finally we found that the simulation results agree better with the theoretical results.(2) Taking into account the real financial system, investors’learning and imitation phenomenon exist in the transaction processes, we investigate the repeating process of the spatial public goods game in this paper. Moreover, having studied Wang et al memory-based snowdrift game on networks, we know that the participants choose their own contrary strategy to do a virtual game and get virtual income, then they make a contrast with the real payoffs and get the better strategy, finally they update the memory vault. Inspired by this process, we have studied memory effect on cooperative behavior in the spatial public goods game model. Before making decisions, participants examine their total payoffs after τ steps, namely by investigating the methods of total payoffs, we can study the individual’s memory effect. Here we defined r as the length of total payoffs. The results of simulation show that, the introduction of this mechanism can promote the cooperation behavior emerging in the spatial PGG. The cooperation level of system will not continue to increase but maintain at a stable value when the length of total payoffs τ reaches a certain value. That means the opposite side’s experience of long time ago is little reference value for the individual.(3) The irrational factors in the real life is exist widely. It’s role is similar to the influence of noise on the system. In this section, the effect of noise intensity on the spatial public goods game behavior is analyzed. The results of simulation show that the noise plays an inhibitory role in the emergence of cooperative behavior, and the inhibitory effect will be more obvious when the multiplication factor is smaller, it shows that the robustness of the system with small multiplication factor is poorer. In addition, the frequency of cooperation changing with the multiplication factor presents step structure when the noise intensity is very small, and each segment corresponds to a unique space pattern. Finally, we explore the reason why the curve presents step structure, theoretical analysis agrees well with the numerical simulation results.