The Minority Game And Majority Game In Econophysics

Finance is playing a more and more important role in people’s business and political activities, and we also see the combination of financial engineering and modern technology have been speed up by the rapid development of finance, forming a multi-discipline science named econophysics.More and more physicists is coming to attend the research of finance problem, they mainly use two ways to do this job. One is to analyze the financial data in a deep degree,exploring the experience rule at the same time; the other is constructing finance model,looking for the relation between agent’s microscopic behavior and macro performance of finance market. Physicists insist that those data of price fluctuation is in fact the result of adaptive regulation from inner system when suffering effect from the outside, the finance data must indicate all the dynamic information of the finance system. So, the physicists may give us some meaningful results and characters.The minority game is such a typical research model. We introduce the basic minority game and evolutionary minority game in order to explain the results and concepts about econophysics game. With the help of complex networks, we get the model which are richer and closer to real life. At last, the majority game born as the time going on is also brought in.All below is my work:(1)The basic minority game is set in complex networks, the agent in the network could know the neighbour’s score and strategy, by comparing the agent’s score and his neighbour’s,the agent will decide whether to use his best neighbour’s best strategy or not. We found that the best neighbour’s best strategy is useful to improve the resource utilization rate when ‘m’is small; If ‘m’ is too large, you’d better not to use neghbour’s strategy.(2)We have proposed a model which the neighbour’s choice forms the information in the current step. We found comparing to the model in the basic minority game which agents use the information made of the record of the winner in last m steps, the variance is reduced greatly.(3)The basic majority game and the evolutionary majority game in which agentsprefer to stay in the majority are put forward on the basis of minority game. All the agents in the model are given bounded rationality, and they compete for finite resources. In the two models, basic majority game has higher utilization using resources when the dimension of the strategy space, m is small. As m gets large, the utilization becomes lower, approaching that of the random choice. While the utilization of evolutionary majority game isn’t affected by m, it is related with r which represents the relation between the new p-values and old p-values, and it’s also related with prize-to-fine R.