共演化博弈动力学中若干关键问题研究

Evolutionary game dynamics has become a hot research issue in the field of complex systems over recent years. In the context of coevolutionary dynamics, this project is mainly concentrated on problems including the evolution of cooperation, the evolution of fairness, and application of evolutionary game theory in the multi-agent systems. In terms of the evolution of cooperation, we explore the effects of different migration patterns on the viability of strategies competing to survive. By virtue of perturbation theory, we derive the frequency of each strategy in the equilibrium, by which we can further establish the conditions under which the frequency of one strategy is larger than that under neutral drift; We next set up a model to analyze the conditions under which the homophily can evolve, and generalize this settings to structured populations, thus providing theoretical explanation for the ubiquity of homophily; Following comes the study on the evolution of parochial altruism. By combination of evolutionary set theory and coalescent theory, we originally explore the conditions, on the level of individual-based selection, for the parochial altruism to evolve. We also consider the coevolution of tag diversity and contingent cooperation, which can induce more studies on games on multiplex networks. This project also explores the effects of role asymmetry in the ultimatum games on the emergence of fairness. Individuals obtain the chance to be proposers by competition. Whoever wins out the competition relies on the cost they pay out, or the frequency that his offering is accepted. This project attempts to resolve the issues in the multi-agent systems with involving the tools and methods in evolutionary game theory, in hope of opening out a new road to analyze and design multi-agent systems.

演化博弈动力学研究是近年来复杂系统中的一个热点问题。在共演化的背景下，本项目主要研究：合作演化的机理、公平演化的机理、演化博弈论在多智体系统中的应用。(1)研究不同的迁移范围对多策略竞争存活的影响，借助摄动理论，给出策略在平稳状态下的频率，进而得出策略优于中性漂移时的条件；研究趋同性演化的条件，并将其推广到结构化的群体中，从理论层面上解释趋同性的广泛存在；研究区域性利他行为的建立，结合演化集合论和溯祖理论，在基于个体选择的层面上，原创性地给出区域性利他行为得以建立的条件；研究标签多样性与条件合作共存的条件，这可以激发多层网络上的博弈动力学研究。(2)探索通牒博弈中角色的非对称性对公平演化的影响。个体通过竞争获得提议者的角色。竞争的结果取决于个体付出的代价，或者个体成功分配资源的频率。(3)尝试用演化博弈论的方法和工具解决多智能体系统的协调与控制问题，为多智能体系统的分析与设计开辟新的途径。

在国家自然科学基金青年基金项目“共演化博弈动力学中若干关键问题研究”（61403293）的支助下，根据项目计划，围绕“博弈共演化”的主线，展开了演化动力学的研究：研究了多群组结构群体中区域利他演化动力学；研究了迁移形式对区域利他策略演化的影响；研究了表型多样性与合作的演化动力学；研究了多标签下的合作演化动力学；研究了惩罚形式在合作演化过程中的重要作用。以上成果已发国际SCI论文5篇，在审1篇，尚有部分成果在整理中，其中“表型多样性与合作的共演化动力学”相关成果得到了美国常春藤名校达特茅斯学院（Dartmouth College）的报道（https://www.sciencedaily.com/releases/2017/02/170203151604.htm）。本项目两名参与硕士已毕业，在读博士一名。