Evolution Effect In Game Model On Small World Network

Financial system is a complex system. The traditional finance can't explain more and more economic phenomena properly. Hence, it attracts much attention among scholars. Econophysics is used to analyze the financial problem with physical conception and method. In econophysics, minority game model is a simple and practical model and it take account of the psychology and behavior of the agents in the financial market, and reflects the phenomenon in many social and biological system that many agents compete for limited resource.It is shown that social networks have obvious small-world characteristics. So, we combine small-world network with minority game to analyze the system's evolutionary property by simulation.First, we give the brief introduction to development of econophysics as well as the minority game model and evolutionary minority game. Next, we discuss the property of network and formation of small-world network. Then, we study the evolution effect of minority game on small-world network.(1) By local information transmission among agents, we study evolutionary minority game on NW small-world network. Simulation results show that the population of the agents also tends to self-segregate into two opposing groups and the dependence of the variance on r is not monotonic. In contrast to WS small-world network, the clustering coefficient of NW small-world network is bigger and the cliquishness of NW small-world network is higher with the same probability PS.(2) Two methods is given to modify the strategy in three-options evolutionary minority game on small-world network. And we calculate the variance for each option with different R and show the distribution P(p₁, p₂) on a grey-scale two dimensional plot, finding that introducing the imitation is advantageous for the system. We also find that the decrease of d value is advantageous to improve the performance of the system for R<0.