复杂结构群体博弈演化时间分布的平均场近似理论

发布时间：2018-06-19 05:36

本文选题：复杂网络 + 演化博弈　；参考：《华东师范大学》2017年硕士论文

【摘要】：频率依赖选择过程是解决演化博弈理论的经典模型。在一个群体中,假设个体仅有两种策略(s_1,s_2)可以选择,并且初始状态设为有一定比例的个体持有策略,在策略密度演化的过程中,关心的一个问题是系统如何到达吸收态。比如,群体中所有个体都持同一策略(s_1或者s_2)。对于尺寸无限大且充分混合的群体,确定性方程能很好描述群体的动力学行为,即可以用常微分方程描述策略密度的演化过程,另外平均演化时间可以很好地描述系统演化速度的快慢。本文主要处理当群体个数有限或者群体具有网络结构时的演化快慢问题。数值模拟结果发现,平均演化时间并不能准确描述群体演化快慢,并且最终到达吸收态的时间步在一个比较大的范围内涨落,当具有网络结构时,这些现象更加明显。为了更好地理解这些现象,本文将策略密度的演化过程看做马尔可夫过程。运用平均场方法,得到策略密度的转移矩阵,进而得到演化时间分布的一般表达式。在不同的博弈模型和网络结构的条件下,我们详细比较了群体从同一初始状态出发,到达吸收态的演化时间分布的差异,提出用标准差来描述演化时间分布的宽度。同时,详细讨论了囚徒困境和协调博弈模型下初始策略密度、平均度、个体理性程度对于演化时间标准差的影响。数值模拟的结果和理论求解相当吻合。
[Abstract]:Frequency dependent selection process is a classical model to solve evolutionary game theory. In a population, it is assumed that there are only two strategies for individuals to choose from, and the initial state is set to a certain proportion of individual holding strategies. During the evolution of strategy density, one of the issues concerned is how the system reaches the absorption state. For example, all individuals in a group have the same strategy: s1 or s2. For a population with infinite size and fully mixed size, deterministic equations can well describe the dynamic behavior of the population, that is, the evolution process of strategy density can be described by ordinary differential equations. In addition, the average evolution time can well describe the speed of the evolution of the system. This paper mainly deals with the problem of the speed of evolution when the number of population is limited or the group has a network structure. The numerical simulation results show that the average evolution time can not accurately describe the population evolution rate and the time step to the absorption state fluctuates in a relatively large range. These phenomena are more obvious when there is a network structure. In order to better understand these phenomena, this paper regards the evolution of strategy density as Markov process. By using the mean field method, the transfer matrix of the strategy density is obtained, and the general expression of the evolution time distribution is obtained. Under different game models and network structure, we compare the difference of evolution time distribution between groups from the same initial state to the absorption state in detail, and propose a standard deviation to describe the width of the evolution time distribution. At the same time, the effects of the initial strategy density, average degree and individual rationality on the standard deviation of evolution time are discussed in detail. The results of numerical simulation are in good agreement with the theoretical solution.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

【相似文献】