复杂适应系统中人群分布相变的统计力学分析  

Statistical Mechanics Analysis of the Phase Transition for Population Distribution in Complex Adaptive Systems

作　　者：汪秉宏[1] 陈侃 苑宝生 

机构地区：[1]中国科学技术大学近代物理系 [2]国立新加坡大学计算科学系

出　　处：《复杂系统与复杂性科学》2004年第4期36-44,共9页Complex Systems and Complexity Science

基　　金：国家自然科学基金项目 (70271070;10472116);高等学校博士点专项科研基金(20020358009)

摘　　要：在引入奖惩比参数R的进化争当少数者博弈模型中,经纪人按策略基因值p的分布从自分离为两个极端人群的相转变为中庸人群峰化相的相变,在R<1的情况下是普遍存在的。这一相变不仅依赖于奖惩比R,还依赖于参与博弈的总人数N,和使经纪人破产更新的最低积累财富阈值d的设定。提出一个仅有 3个基因p值(仅取p=0, 1/2, 1)的EMG模型,其判断胜负和经纪人记分的规则完全相同于通常的争当少数者博弈模型。发现:简单的只有 3个策略基因p值的EMG模型所揭示的临界经纪人总数Nc所遵从的规律居然很好地适用于连续p的EMG模型的相变。给出一个统计力学理论,对于人群分布相变点计算公式给出完全的解释。We found that in the evolutionary minority game (EMG) with prize-to-fine ratio, R less than 1, transition behavior from self-segregation phase (into opposing groups) to clustering phase (swarming towards cautious group) are universal. The critical point of phase transition depends on not only prize-to-fine ratio R, but also the total number of agents N and the threshold value d of accumulated wealth for agent bankruptcy. We study a simple model for EMG with only three different gene values for strategy(p=0, 1/2, 1)using a statistical mechanics approach. A theory for the steady-state population distribution of the agents is derived based on an ‘adiabatic approximation’ in which the short time fluctuations in the population distribution are integrated out to obtain the effective equation governing the steady-state distribution. It is surprising that the phase transition critical point as the function of the parameters R, N, and d revealed by simple model with only three p values can be applied very well to phase transition in the general EMG model with continuous p value. The transition is determined by two generic factors: the market impact (of the agents′ own actions) and the short time market inefficiency (arbitrage opportunities) due to the fluctuations in the numbers of agents using the opposite strategies. Large market impact favors ‘extreme’ players who choose fixed opposite strategies, while large market inefficiency favors cautious players. The transition depends on the effective rate of strategy switching. When the number of agent N is small, the market impact is relatively large; this favors the extreme behaviors. Frequent strategy switching, on the other hand, leads to clustering of the cautious agents.

关 键 词：复杂适应系统 争当少数者博弈模型 人群分布相变 统计力学中的绝热近似法 

分 类 号：N941[自然科学总论—系统科学] O225[理学—运筹学与控制论]