【摘要】：演化博弈論研究的是競爭個體之間相互作用的模型,它廣泛應用于生物學,經(jīng)濟學,和其他社會科學等方面.現(xiàn)階段,研究的博弈主要都被建模在單種群的生態(tài)學方面,單種群演化博弈模型的研究可以解決一個大的種群中個體之間存在矛盾、競爭和合作等問題,然而,不同的生物種群中的個體也可能會相互作用,并且這種現(xiàn)象在實際生活中更為普遍,通過研究多種群的演化博弈理論可以對生態(tài)演化、自組織涌現(xiàn)行為、網(wǎng)絡化系統(tǒng)、經(jīng)濟動力學等多方面的研究起到強大的作用.因此研究多個種群的演化博弈模型是一件非常有意義的工作.本文共分為四章.第一章緒論主要論述了本文的研究背景、研究意義、目前研究現(xiàn)狀、主要內(nèi)容以及使用工具和創(chuàng)新點.第二章是單種群博弈的演化博弈問題研究.第三章是多種群博弈的演化博弈模型研究.第四章是結(jié)論與展望.本文的主要研究工作如下:(1)推廣了單種群單態(tài)演化博弈中演化穩(wěn)定鄰域入侵策略的概念和相關(guān)性質(zhì),從而解決了單種群二態(tài)演化博弈中演化穩(wěn)定策略的動態(tài)可達性問題,并用實例進行了驗證.(2)建立了多種群演化博弈模型,將單種群演化博弈模型中相關(guān)理論延拓到多種群博弈中,在多種群非對稱博弈中給出了演化穩(wěn)定鄰域入侵策略概念,分析了演化穩(wěn)定策略的動態(tài)可達性問題,在突變和自然選擇的共同作用下,多種群演化博弈存在一個演化穩(wěn)定鄰域入侵策略.
[Abstract]:Evolutionary game theory studies the model of interaction between competitive individuals, which is widely used in biology, economics, and other social sciences. At present, the game studied is mainly modeled in the ecology of single population. The study of single population evolutionary game model can solve the problems of contradiction, competition and cooperation among individuals in a large population. Individuals in different biological populations may also interact, and this phenomenon is more common in real life. Through the study of multi-population evolutionary game theory, ecological evolution, self-organizing emergence behavior, networked systems can be studied. Economic dynamics and other aspects of the study play a strong role. Therefore, it is a very meaningful work to study the evolutionary game model of multiple populations. This paper is divided into four chapters. The first chapter mainly discusses the research background, research significance, current research status, main content, the use of tools and innovation. The second chapter is the evolutionary game problem of single population game. The third chapter is the evolutionary game model of multi-population game. The fourth chapter is the conclusion and prospect. The main research work of this paper is as follows: (1) the concept and related properties of evolutionary stable neighborhood intrusion strategy in single population singlet evolutionary game are extended, and the dynamic reachability of evolutionary stability strategy in single population binary evolutionary game is solved. An example is given to verify it. (2) A variety of group evolutionary game models are established, the related theories in the single population evolutionary game model are extended to a variety of group games, and the concept of evolutionary stable neighborhood intrusion strategy is given in a variety of group asymmetric games. The dynamic reachability of evolutionary stability strategy is analyzed. Under the combined action of mutation and natural selection, there is an evolutionary stable neighborhood intrusion strategy in multiple group evolutionary games.
【學位授予單位】：遼寧師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O225

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