本文選題：復(fù)雜網(wǎng)絡(luò) + 演化博弈�。� 參考：《華東師范大學(xué)》2017年碩士論文

【摘要】：頻率依賴選擇過程是解決演化博弈理論的經(jīng)典模型。在一個(gè)群體中,假設(shè)個(gè)體僅有兩種策略(s_1,s_2)可以選擇,并且初始狀態(tài)設(shè)為有一定比例的個(gè)體持有策略,在策略密度演化的過程中,關(guān)心的一個(gè)問題是系統(tǒng)如何到達(dá)吸收態(tài)。比如,群體中所有個(gè)體都持同一策略(s_1或者s_2)。對(duì)于尺寸無限大且充分混合的群體,確定性方程能很好描述群體的動(dòng)力學(xué)行為,即可以用常微分方程描述策略密度的演化過程,另外平均演化時(shí)間可以很好地描述系統(tǒng)演化速度的快慢。本文主要處理當(dāng)群體個(gè)數(shù)有限或者群體具有網(wǎng)絡(luò)結(jié)構(gòu)時(shí)的演化快慢問題。數(shù)值模擬結(jié)果發(fā)現(xiàn),平均演化時(shí)間并不能準(zhǔn)確描述群體演化快慢,并且最終到達(dá)吸收態(tài)的時(shí)間步在一個(gè)比較大的范圍內(nèi)漲落,當(dāng)具有網(wǎng)絡(luò)結(jié)構(gòu)時(shí),這些現(xiàn)象更加明顯。為了更好地理解這些現(xiàn)象,本文將策略密度的演化過程看做馬爾可夫過程。運(yùn)用平均場(chǎng)方法,得到策略密度的轉(zhuǎn)移矩陣,進(jìn)而得到演化時(shí)間分布的一般表達(dá)式。在不同的博弈模型和網(wǎng)絡(luò)結(jié)構(gòu)的條件下,我們?cè)敿?xì)比較了群體從同一初始狀態(tài)出發(fā),到達(dá)吸收態(tài)的演化時(shí)間分布的差異,提出用標(biāo)準(zhǔn)差來描述演化時(shí)間分布的寬度。同時(shí),詳細(xì)討論了囚徒困境和協(xié)調(diào)博弈模型下初始策略密度、平均度、個(gè)體理性程度對(duì)于演化時(shí)間標(biāo)準(zhǔn)差的影響。數(shù)值模擬的結(jié)果和理論求解相當(dāng)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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

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