Evolution Minority Game On The Evolutionary Small-world Networks

At the end of last century, the scientists in different fields were more and more concernedabout the complex phenomena that appeared in the human and natural world. And then a newinterdisciplinary science field-complex nonlinear disciplines was formed. The financialsystem as an important part of human activities, due to its typical nonlinear complex featuresspikes fat tail, sheep effect and some other phenomenon that cannot reasonably beexplained by the traditional economics, attracted the attention of the scientists in various fields,particular, the scientists of mathematics, physics, economics, psychology, and computerscience.D.Challet and YC.Zhang proposed the "Minority Game" model (MG) on the basis of the"EL Farol Bar" problem. Though its structure and rules is simple, it reflects the complexbehavior of agents competing for a small number of limited resources and attracts people’sattention. Since then, more and more researches were done. The most realistic financialmarkets model is the minority game on small-world networks, because researches show thatthe real-world is not simply a random networks or regular networks, it is a small-worldnetworks.In this paper, we introduce the developing minority game models as well as the keyparameters which influence the model, and a minority game on small-world networks.(1) For the minority game, we introduced "Δ"—the difference between the number of"majority party" and "minority party"—as an extra information, a part of the agents wereallowed to use this extra information means these agents own more information, so it is aasymmetric information game. Finally we found that, a certain range of agents use the extrainformation makes their success rate higher than the others, while exceed the range; theirsuccess rate gets lower than the others.(2) Minority game on small-world networks was evolved. The time-varying small-worldnetworks were introduced since the real-world interpersonal characteristics change over time.Taking into account the real-financial market that the winner gains always related-to the loss of the failure, we defined the prize-to-fine R:R (t)=max(num(1,t),num(0,t))min(num(1,t),num(0,t))From the simulation we found that, a) the system variance has a certain reduction if weintroduced “the small-world networks change over time”, b) As the prize-to-fine R(t)introduced else, the system variance was reduced a lot.(3) The imitation effect in a modified evolutionary minority game on NW small-networkswas studied. We found that the self-segregation occurred; the system variance depends on thehistorical record length m and the rewiring probability ps. The system variance is minimum atm=1; as m increasing, the variance increases and finally approaches to that of random choose.Also we found the larger rewiring probability leads lager system variance.