广西师范大学学报(自然科学版) ›› 2016, Vol. 34 ›› Issue (2): 1-7.doi: 10.16088/j.issn.1001-6600.2016.02.001

• •    下一篇

多数者博弈模型演化分析

孙康, 全宏俊   

  1. 华南理工大学物理系,广东广州510641
  • 收稿日期:2016-12-15 出版日期:2016-06-25 发布日期:2018-09-14
  • 通讯作者: 全宏俊(1958—),男,湖南衡阳人,华南理工大学教授,博士。E-mail:hjquan@scut.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11174083)

Evolutionary Analysis of the Majority Game

SUN Kang, QUAN Hongjun   

  1. Department of Physics, South China University of Technology, Guangzhou Guangdong 510641, China
  • Received:2016-12-15 Online:2016-06-25 Published:2018-09-14

摘要: 为研究经纪人行为策略对社会经济复杂系统的影响,本文在少数者博弈模型的基础上提出多数方获胜的基本多数者博弈模型以及演化多数者博弈模型。采用多主体建模方法,模型中的众多经纪人被赋予有限理性,他们可以选择自己的最优策略或者调整策略概率来竞争有限资源,演化到稳态后也能表现出人类社会系统所独有的现象。在基本少数者博弈中,当模型中的游戏规则变为多数方获胜时,得到的基本多数者博弈模型可以更快演化到稳定状态。并且在历史记忆长度m较小的时候系统资源利用率较高,随着m增大资源利用率逐渐降低,最终与经纪人随机选择得到的结果一致。而演化多数者博弈模型的资源利用率则不受m影响,因此在m较大时,引入演化能提高资源利用率。同样的系统参数,随机初始条件不同演化多数者博弈模型经纪人概率也有可能分布在p=0.5不同侧。同时发现,稳定后每时步平均获胜方人数与经纪人概率分布也有联系,在经纪人概率重置时采用不同的边界条件,得到的经纪人概率分布也不同。进一步分析演化多数者博弈模型系统资源利用率,发现经纪人新旧策略概率的相关程度r越大,概率分布越平坦,系统资源利用率越高。增加奖惩比R,也会影响经纪人概率分布,资源利用率也会提高。

关键词: 行为策略, 少数者博弈模型, 基本多数者博弈模型, 演化多数者博弈模型, 有限理性

Abstract: In order to study the influence of agents’ action strategies on the evolution of social economic system, the basic majority game and the evolutionary majority game in which agents prefer to stay in the majority are put forward on the basis of minority game. We build agent-based models,all the agents in the model are given bounded rationality, and they use their best strategy or modify their strategy probility each round in order to compete for finite resources. When evolving to stable state, phenomena which are unique to human society also occur. In the basic minority game, if agents in the majority are ruled winners, we get the basic majority game,and the game has higher resources utilization when the dimension of the strategy space, m, is smaller. As m gets larger, the utilization becomes lower, approaching that of the random choice game finally. While the utilization of evolutionary majority game isn’t affected by m, so,when m in the game is larger,the evolution is so perferable to improve the utilization of the system. With the same parameters in the game,different random initial conditions may cause different side of distribution of P(p) at p=0.5.The average number of winners each round is also found to be related to the distribution of P(p) at the same time. If we use different boundary conditions to reset agents’ strategy probabilities, we will also get different distribution of P(p). For further analysis of evolutionary majority game’s utilization, we find that the lager the parameter r which means the relation between agents’ old and new p,the flatter distribution of P(p) is,and the utilization also gets larger.At last, if we improve R representing the value of the prize-to-fine ratio, the distribution of P(p) will also be affected,resulted to a lager utilization of the game.

Key words: action strategies, minority game, basic majority game, evolutionary majority game, bounded rationality

中图分类号: 

  • O414.2
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