具有网络结构的演化博弈动力学

项目名称： 具有网络结构的演化博弈动力学

项目编号： No.11301032

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 张博宇

作者单位： 北京师范大学

项目金额： 22万元

中文摘要： 演化博弈理论结合了进化生物学和经济学思想，以有限理性为基础，从动态角度对个体行为（策略）进行研究。演化博弈动力学是演化博弈的数学基础。在无限大且均匀混合的种群中，个体行为随时间变化的规律可以通过复制方程描述。在真实的种群中，个体间相互作用的机会并非完全均等。一般意义下，这种关系可以通过复杂网络方法表示。个体间相互作用的网络结构如何对行为演化产生影响是演化博弈最为重要的理论问题之一。大量计算机数值模拟结果表明网络结构会极大的改变行为的演化，而这些结果背后的理论机制尚不清楚。本研究将应用随机动力学方法和确定性动力学方法，构建包含网络异质性的演化博弈动态，深入分析网络结构对进化稳定性的影响。这些研究结果不仅会对演化博弈理论的完善和发展做出有意义的贡献，同时还将为解释生态现象和经济现象提供新的理论视角。

中文关键词： 演化博弈；种群动力学；空间结构；不同的更新规则；

英文摘要： Evolutionary game theory (EGT) is the application of game theory to evolutionary biology. In the context of boundedly rationality, EGT focuses on the dynamics of individual behavior (which is expressed as "strategy") change. Evolutionary game dynamics is the study of mathematical principles according to evolutionary rules and mechanisms. In an infinite well-mixed population where all individuals have equal chances to interact with everyone else, the evolution of the frequencies of strategies can be described by the replicator equation. However, in more realistic population, different individuals interact with different subsets of the whole population. This kind of structures is generally described by means of complex networks. How the evolutionary process is affected by network structure is one of the most important theoretical problems in EGT. A great deal of research based on numerical simulations has been devoted to explain the influence of network structure on evolution, but there is lack of analytical studies. In this project, evolutionary dynamics on heterogeneous network will be established by apply stochastic approach and deterministic approach, and the dynamical properties of the resulting systems will be analyzed in detail. Our main goal is to reveal the effects of network structure on evolutionary sta

英文关键词： evolutionary game；population dynamics；spatial structure；different updating rules；