矩阵的半张量积在网络演化博弈中的应用与逻辑算子的张量表示

发布时间：2018-01-10 00:03

本文关键词：矩阵的半张量积在网络演化博弈中的应用与逻辑算子的张量表示　出处：《聊城大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文利用矩阵的半张量积理论,研究了进化博弈论中的进化稳定策略.另外,利用张量与矩阵的乘法法则,将逻辑算子的矩阵表示转化为逻辑算子的张量表示.同时,对于变异雪堆博弈在网络演化博弈中的模型中的动态演化历程进行了研究.此外还研究了基于社会惩罚的囚徒困境博弈的网络演化博弈模型与控制问题,加入控制序列来讨论其动态行为.本文做的主要工作有:(一)研究了进化博弈中进化稳定策略的求解问题.利用伪布尔函数性质,给出了有限理性下的进化博弈基本分析模型中进化稳定策略的一种新求法.(二)研究了逻辑算子的张量表示方法.在张量与矩阵的乘法运算规则下,利用逻辑算子的真值表得出相应逻辑算子的张量表示.(三)建立了添加回报机制的变异雪堆博弈的网络演化模型,结合逻辑动态系统,再转成代数形式,讨论其最终合作稳定性.(四)研究了具有社会惩罚的进化网络博弈,得到了进化动态博弈的代数形式.得到了一个设计自由类控制序列的充要条件使所有局中人合作。
[Abstract]:By using the semi tensor product of matrices theory, study the evolutionary stable strategy in evolutionary game theory. In addition, the rule of tensor and matrix multiplication, matrix representation of logical operators into tensor logic operators. At the same time, the variation in the snowdrift game is studied in the dynamic evolution process of network evolution in the game model.. in addition, the paper studies the model and control of game of prisoner's dilemma game network evolution based on social punishment, adding control sequence to discuss its dynamic behavior. The main works of this paper are: (a) the study of problem solving into evolutionary stable strategy in the game. By using the properties of pseudo Boolean functions, given the evolutionary game Co. the basic reason analysis of a new method for solving the evolutionary stable strategy model. (two) said the tensor method to research logical operator. The tensor and matrix multiplication. Then, using the logic operator truth table that tensor corresponding logic operators. (three) established the evolution model of variation mechanism of the snowdrift game add return network, combined with the logic of dynamic system, then turn into algebra, and discuss its final cooperation stability. (four) studied the evolution of network game social punishment has obtained the algebraic form of evolutionary dynamic game. Get a free class design to control the sequence of necessary and sufficient conditions for all the people in the game.

【学位授予单位】：聊城大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21;O183.2

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