小世界网络上的自我质疑动力学演化博弈  

Self-questioning dynamical evolutionary game in small-world networks

作　　者：杨波 张永文 刘文奇 陈晓松[3,4] YANG Bo;ZHANG YongWen;LIU WenQi;CHEN XiaoSong(Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, China;Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China;Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China)

机构地区：[1]昆明理工大学数据科学研究中心,昆明650500 [2]昆明理工大学理学院,昆明650500 [3]中国科学院理论物理研究所理论物理前沿重点实验室,北京100190 [4]中国科学院大学物理科学学院,北京100049

出　　处：《中国科学：物理学、力学、天文学》2018年第5期9-20,共12页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:61573173);昆明理工大学引进人才科研启动基金(编号:KKSY201607047)资助

摘　　要：自我质疑更新规则是博弈个体对比各备选策略所得收益后选出最优策略的过程.本文研究小世界网络上一类具有利他或恶意伤害属性的自我质疑演化博弈.为获得长程连接和度的异质性对演化博弈模型的影响,我们分别研究二维正方格子、以正方格子为基础构造的同质小世界网络(度分布不发生改变,仅仅引入长程连接)和异质小世界网络(既有长程边也有度的异质性)三类空间结构.通过Ising模型相变理论和蒙特卡罗模拟获得以下结论:长程连接使博弈个体出现矛盾选择状态,类似于物理中的阻挫;度的异质性会影响作用在博弈个体上的外场,邻居越多外场越大;当存在正向外场时,长程连接促进合作的产生,而度的异质性抑制合作的产生.Self-questioning update rules is the selected process of the optimal strategy of the individuals by comparing the payoff from various alternative strategies. In this paper, a self-questioning dynamical evolutionary game with altruistic or spiteful preferences via weighted sums of own and opponent’s payoffs is studied. In order to obtain the influence of longrange connections and degree heterogeneity on evolutionary game model, we study three kinds of spatial structure： the two-dimensional lattice, homogeneous small-world networks（only the introduction of long-range connections） and heterogenous small-world networks（both long-range connections and degree heterogeneity）. Through the Ising model theory and Monte Carlo simulation the following conclusions are obtained： long-range connections make the individuals perplex in strategic choice which is similar to the state of frustration in spin glass; the degree heterogeneity makes the different individual has the different field（the more neighbours, the larger of field）; when the field is positive, long-range connections promote cooperation, but the heterogeneity of degree inhibits the production of cooperation.

关 键 词：ISING模型 蒙特卡罗模拟 自我质疑更新规则 

分 类 号：O225[理学—运筹学与控制论]