基于间接互惠的演化动力学中声望共享系统的建立

Indirect reciprocity (I help you today, and somebody will help me tomorrow) plays the most important role in accomplishing cooperation during various businesses. Evolutionary game theory provides a mathematical framework for studying how indirect reciprocity influences the evolution of cooperation. Two problems have been demonstrated: 1. finite populations give rise to a large difficulty for theoretical analysis of indirect reciprocity，and there are very few results thereof; 2. if the cost incurred by sharing others' reputation is introduced, individual's reputation will not be shared among the whole population any more, and cooperation will not be evolved from indirect reciprocity. The coalescence theory will be combined with the theory of the random walk to overcome the analytic difficulty of indirect reciprocity in finite populations. The method is used to investigate social phenomena in group-structured populations, e.g., local migration and local disperse of reputation, and brings about quantities of opportunities for the study of indirect reciprocity. New assessment modules of reputation meaning that individual's reputation is up to his behavior as the donator and that as the observer will be constructed. The module which not only allows for the existence of reputation sharing system but also favors the evolution of cooperation will be obtained in well-mixed populations of infinite size and group-structured populations of finite size. It can diminish the phenomena “only buy but not assess”, and can improve the environment of online shopping. The results will provide the study of how indirect reciprocity influences the evolution of cooperation with new methods and new ideas.

间接互惠(今天我帮助你，明天他会帮助我)在处理事务、达成合作的过程中占据最为核心的地位。演化博弈论为研究间接互惠如何影响合作的涌现提供了数学框架。众多研究表明：a 有限群体为间接互惠带来巨大解析困难，相关的理论分析甚少；b 共享某人声望所需成本导致个人声望无法在群体中共享，从而基于间接互惠的合作行为无从涌现。本项目将溯祖理论和随机游走理论巧妙结合，克服有限群体为间接互惠带来的解析难题。此方法可被用来分析社区结构群体中局部迁移和声望的局部传播等现象，为丰富关于间接互惠的研究提供众多机遇。本项目基于经典的声望评估准则，将玩家作为观察者的表现纳入对其声望的评价，构建新的评估准则。在无限混合均匀和有限社区结构群体中，获得既能建立声望共享系统又能促进合作涌现的准则。此准则可以避免电子商务中“只买不评”的现象，利于营造诚信的网购环境。本项目成果将为关于间接互惠如何促进合作涌现的研究提供新方法和新思路。

有限群体为间接互惠带来巨大解析困难，相关理论分析甚少。共享某人声望所需成本导致个人声望无法在群体中共享，从而基于间接互惠的合作行为无从涌现。此项目针对这两个问题，进行了以下四方面工作。其一，利用嵌入式马尔可夫链构建了一个有限群体间接互惠的理论分析框架：从两个时间尺度追踪个体声望变化和个体策略演化。具体而言，计算群体中声望的稳态分布，在此基础上利用嵌入式马尔可夫链计算群体中策略的稳态分布。其二，提出融入不同声望传播方式的模型，并给出既能建立声望共享系统又能促进合作涌现的声望传播方式：多值八卦中最小值更新方式、部分接受八卦的态度、单向八卦方向。其三，提出融入共享声望所需成本的模型，并给出既能建立声望共享系统又能促进合作涌现的机制：奖励观察者机制、惩罚观察者机制、基于声望的断边重连机制。其四，建立一种任意迁移模式下社区结构群体中离散策略和连续策略的理论分析框架：利用溯祖理论和随机游走理论对微观个体的决策模式和个体间交互模式进行追踪。据此发现促进合作或公平演化的机制：策略多样性，随机性，断边与重连机制，实验广泛关注的恶意、非单调拒绝、共鸣、配置资源。本项目在有限群体间接互惠的理论方法和机制设计方面取得创新性成果，从而推动演化博弈论的发展和完善。在本项目的资助下，发表SCI国际期刊论文11篇，EI论文5篇，协助指导硕士研究生2名，博士研究生2名。

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