自我质疑机制下公共物品博弈模型的相变特性

发布时间：2018-06-23 23:23

  本文选题：Ising模型 + 有限尺度标度理论　； 参考：《物理学报》2017年19期

【摘要】：公共物品博弈是研究群体相互作用的经典模型,广泛用于解释自私个体间合作的涌现和保持.本文从理论分析和蒙特卡罗模拟两个方面研究了二维正方格子上一个有偿惩罚机制下随自我质疑更新规则演化的公共物品博弈模型的相变特性.理论分析方面,将公共物品博弈模型转化为一个外场不为零的铁磁Ising模型.通过有效能量发现:不存在惩罚时,个体间的耦合强度为零,体系只有外场作用;存在惩罚时,个体间包含最近邻、次近邻和第三近邻相互作用且外场不为零.蒙特卡罗模拟方面,首先验证了理论分析的正确性,然后对公共物品博弈模型相关的一级相变和二级相变进行了有限尺度标度分析.研究发现:1)蒙特卡罗模拟所得结果与类Ising模型分析结果完全吻合;2)相比二维Ising模型,公共物品博弈的二级相变临界指数发生了变化;3)公共物品博弈的一级相变与二维Ising模型相同.
[Abstract]:Public goods game is a classical model to study group interaction, which is widely used to explain the emergence and maintenance of selfish individual cooperation. In this paper, the phase transition characteristics of the game model of public goods evolving with the rules of self-challenge renewal under a paid punishment mechanism on a two-dimensional square lattice are studied from two aspects of theoretical analysis and Monte Carlo simulation. In theoretical analysis, the game model of public goods is transformed into a ferromagnetic Ising model with non-zero external field. It is found by effective energy that the coupling strength between individuals is zero when there is no punishment, and the system only has the external field action, and when there is punishment, the interaction between individuals includes the nearest neighbor, the second nearest neighbor and the third nearest neighbor, and the external field is not zero. In Monte Carlo simulation, the correctness of the theoretical analysis is first verified, and then the first-order and second-order phase transitions related to the game model of public goods are analyzed on a finite scale. It is found that the results obtained from Monte Carlo simulation are in good agreement with those of Ising-like model, and the results of two-dimension Ising model are in good agreement with those of two-dimension Ising model. The second order critical exponent of public goods game has changed 3) the first order phase transition of public goods game is the same as that of two dimensional Ising model.
【作者单位】： 昆明理工大学数据科学研究中心;昆明理工大学理学院;中国科学院理论物理研究所理论物理前沿重点实验室;中国科学院大学物理科学学院;
【基金】：昆明理工大学引进人才科研启动基金项目(批准号:KKSY201607047) 国家自然科学基金(批准号:61573173)资助的课题~~
【分类号】：O469
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本文编号：2058882