The Model Of The Monority Game And The Application In Financial Market

People often encounter such selection problems, many participants faced two choices, if less people choose the choice, then the less people well success. Without considering moral factors, how to make decisions is minority game.The first one who brings forward the non-mathematics game theory to indicate the minority game and conducts the research is Zhang YiCheng, presently settles down in Switzerland's Chinese, and D.Challet. The basic minority game model (BMG) assumes N agents(N is odd), each agent has m-step memory and each agent's strategy set has S strategy. At each round, all the agents would select a strategy from their own strategy set separately and take the action according to the active strategy(the one selected). After all participants complete the decision, the minority side wins. The strategy making the correct instruction as well as the agents who take the win action could gain the point set beforehand. Otherwise, deduct the point. There also have some other modified minority games.According to the above model, we got some important conclusions, In case g x = sgn(x), provide the population N is large enough to assure NS ? 2P, the MG can be describer in terms of the Markov process with the finite number of states. In practical terms this approach is tough for m > 1 due to the large states. For the proportional payoff g(x) = x, stochasticity of transitions disappears but one still observes periodicity, the periodicity is T = 2m+1. The aggregate demand and the strategy have relation|A| = N(1 1/2S 1 ). Moreover, for those two payoffs, they have some similar characteristics, first, with the memory length m increases, the aggregate demand's oscillation decrease. Second, the utility is bounded. Third, the process is Markovian process. Finally, we used the minority game to the European option pricing.The game theory has widespread application in many aspects such as natural, social or economy and has great research prospects. For example, we give the probability of the state, but we failed to find any relation between the memory length m and total number of states.