Study On The Efficiency Of The Minority Game With Different Payoff Functions

In the minority game, a great number of agents compete for the limited resources,using their own strategies adaptively. This complex system has been applied to manyresearch fields, such as financial market, network congestion, and so on.This thesis focuses on the efficiency of minority game with different payofffunctions. Most previous researches employ the step payoff functions evaluating thestrategies used by agents. This thesis introduces line payoff function and quadraticpayoff function to the basic model of minority game, and analyzing the effects ofpayoff functions on the system efficiencies. First, this thesis reviews the features of thebasic minority game with step payoff function, especially the efficiencies. The systemefficiency can be measured by variance, and the smaller the variance gives the higherthe efficiency. Second, this thesis studies the features and efficiencies of the minoritygames with line payoff function and quadratic payoff function. The results reveal thatsome features of the games indeed depend on the forms of the payoff functions,although other features remain unchanged. The dependence of the system efficiency onthe system complexity is related to the diversity. In the case of zero or very smalldiversity, the different payoff functions do not affect the dependence of the variance onthe complexity. However, the different payoff functions will affect the systemefficiency with the increasing diversity.