本文選題：雪堆 + 博弈�。� 參考：《浙江大學(xué)》2017年博士論文

【摘要】：競爭性群體當(dāng)中的合作行為研究是當(dāng)今一個(gè)重要且緊迫的跨學(xué)科難題。目前為止,博弈論提供了最為有效的框架。在合作演化博弈建模中,囚徒困境博弈備受學(xué)界關(guān)注,相比之下雪堆博弈模型的相關(guān)研究較少,而后者通常被認(rèn)為是在描述競爭情景時(shí)前者的替代模型。本文作者在前人研究基礎(chǔ)上,對雪堆博弈模型進(jìn)行了進(jìn)一步的推廣和創(chuàng)新,在N人雪堆博弈模型中引入第三種策略,使用動力學(xué)方程推導(dǎo)和仿真模擬的方法進(jìn)行研究。論文發(fā)現(xiàn)N人雪堆博弈不同于公共品博弈(即囚徒困境的N人博弈推廣模型),呈現(xiàn)出特殊的動力學(xué)性質(zhì),公共品博弈模型的動力學(xué)演化為不同狀態(tài)之間的循環(huán)轉(zhuǎn)化,無法達(dá)到某種穩(wěn)態(tài),而N人雪堆博弈在充分演化的條件下,系統(tǒng)最終可能趨于幾種(兩種或三種)不同性質(zhì)的穩(wěn)態(tài),為研究群體合作行為的演化提供了新的線索。引入利他懲罰機(jī)制的演化博弈研究之前只是在2人博弈的條件下進(jìn)行,論文第二章首次將利他懲罰機(jī)制引入兩策略的N人雪堆博弈模型,建立了含懲罰機(jī)制的三策略N人雪堆博弈模型,并且研究了懲罰機(jī)制的引入對N人雪堆模型在混合均勻群體中造成的影響。作者給出了一系列描述三策略模型的動力學(xué)方程。在充分演化的情況下,系統(tǒng)最終會演化為某種穩(wěn)態(tài),穩(wěn)態(tài)分為兩種,具有不同的特性。一般說來,給定相對較小的本益比r,較大的博弈小組規(guī)模Ⅳ,較大的乘數(shù)因子β/α容易壓制背叛者的滋生,導(dǎo)致系統(tǒng)演化成為一個(gè)合作性質(zhì)的、僅由合作者和懲罰者構(gòu)成的群體,由于所有的背叛者都完成轉(zhuǎn)化,C、P的收益完全相等,系統(tǒng)動力學(xué)凍結(jié),這種穩(wěn)態(tài)被稱為凍結(jié)態(tài),凍結(jié)態(tài)的C、P頻率構(gòu)成取決于初始狀態(tài)。反之,較大的r ,較小的Ⅳ和β/α容易使懲罰者處于一種自毀的發(fā)展模式,懲罰者逐漸消亡,系統(tǒng)演化為一個(gè)僅由合作者和背叛者構(gòu)成的群體,群體繼續(xù)演化,相當(dāng)于最初的兩策略N人雪堆博弈模型的動力學(xué)演化,最終達(dá)到活動態(tài)。因此,活動態(tài)的C、D頻率構(gòu)成與初始狀態(tài)無關(guān),同時(shí)也與懲罰者相關(guān)的參數(shù)設(shè)定無關(guān)。論文作者進(jìn)一步提出了完全描述系統(tǒng)演化動力學(xué)過程的模擬算法,經(jīng)驗(yàn)證復(fù)制動力學(xué)方程與程序模擬的結(jié)果高度一致。第三章中作者通過在原始兩策略NSG模型中引入額外的L策略,研究并建立了一個(gè)三策略N人雪堆博弈模型。論文推導(dǎo)了混合均勻群體結(jié)構(gòu)下三種策略頻率的動力學(xué)方程。給定任何初始條件,都可以通過迭代動力學(xué)方程獲得頻率的時(shí)間演化及其穩(wěn)態(tài)分布。模型參數(shù)即本益比r和固定收益L的不同取值導(dǎo)致了系統(tǒng)豐富的演化行為。對顯示系統(tǒng)如何演變的三角流向圖的詳細(xì)研究表明,根據(jù)模型參數(shù)取值不同,穩(wěn)態(tài)可以是AllL,AllC或C + D態(tài)中的一種。策略L的引入起到了兩個(gè)作用。它有助于引導(dǎo)系統(tǒng)達(dá)到All L態(tài),也有助于達(dá)到All C態(tài)。相比之下,將利他懲罰機(jī)制(P策略)引入N人雪堆博弈只能導(dǎo)致兩種策略混合的穩(wěn)態(tài)。此外作者同樣使用了一種仿真模擬算法作為理論研究結(jié)果的驗(yàn)證,這種算法可用于對各種結(jié)構(gòu)性群體中的NSG模型研究。第四章中,論文作者在可選雪堆博弈模型(Optional NSG)基礎(chǔ)上增加了一個(gè)合作人數(shù)的下限閾值T。論文給出了該模型的動力學(xué)方程,同樣也用模擬算法進(jìn)行驗(yàn)證。和OptionalNSG模型類似,新的模r*同樣存在一個(gè)臨界值r*將系統(tǒng)分為兩種最終穩(wěn)態(tài),當(dāng)rr*的時(shí)候,系統(tǒng)終態(tài)表現(xiàn)為C、D共存的活動態(tài),當(dāng)rr*的時(shí)候,系統(tǒng)終態(tài)表現(xiàn)為ALLL的凍結(jié)態(tài)。當(dāng)設(shè)定下限閾值為2時(shí),對群體最后達(dá)成C、D共存起到了積極的作用。但是當(dāng)下限閾值繼續(xù)提高時(shí),反倒對合作產(chǎn)生了抑制作用。在N=T的特殊情況下,背叛者永遠(yuǎn)不可能通過利用合作者而獲取收益,從而背叛者成為了弱勢群體。系統(tǒng)在這樣的背景下最終也會演化為兩種狀態(tài)ALL C和ALL L,而不再有C、D共存的終態(tài),某種程度上促使D向C轉(zhuǎn)變,最終消滅了 D策略。第五章中,論文作者在OptionalNSG模型的基礎(chǔ)上,再度引入了懲罰機(jī)制,將模型擴(kuò)展為一個(gè)N人四策略博弈模型。論文給出了該模型的動力學(xué)方程,并通過迭代動力學(xué)方程和算法模擬,得出有關(guān)該模型性質(zhì)的一些初步結(jié)論。和之前的模型類似,N人四策略雪堆博弈模型同樣存在一個(gè)臨界值r·*表達(dá)系統(tǒng)最終穩(wěn)態(tài)的突變。當(dāng)rr*的時(shí)候,隨著r的增加,系統(tǒng)終態(tài)依次表現(xiàn)為C、P共存,C、D、P共存和C、D共存的活動態(tài),這種變化是連續(xù)的。當(dāng)rr*的時(shí)候,系統(tǒng)終態(tài)突變?yōu)锳LLL的凍結(jié)態(tài)。這種相態(tài)的轉(zhuǎn)變是瞬變,而非逐漸變化。論文就各參數(shù)對于最終穩(wěn)態(tài)造成的影響進(jìn)行研究發(fā)現(xiàn),L的增大使得瞬變的關(guān)鍵點(diǎn)r*提前到來,β的增大使得懲罰力度增加,而N的增大給背叛者利用合作者的勞動成果提供了機(jī)會,使得合作的難度增加,。
[Abstract]:The study of cooperative behavior among competitive groups is an important and urgent interdisciplinary problem. So far, the game theory provides the most effective framework. In the cooperative evolutionary game modeling, the prisoner's dilemma game has attracted much attention, compared with the research of the snow pile game model, and the latter is usually considered to be in the description. On the basis of previous studies, the author further popularized and innovating the snow pile game model on the basis of previous studies, introduced third strategies in the N man snow game model, and studied the use of Dynamic Equation Derivation and Simulation simulation. The paper found that the N snow pile game is different from public goods. The N game extension model of the prisoner's dilemma presents a special dynamic character. The dynamics of the game model of the public goods is transformed into a cycle between different states and can not reach a certain steady state. While the N man snow pile game is fully evolved, the system may eventually tend to several (two or three) different properties of the steady state. In order to study the evolution of group cooperative behavior, the evolutionary game of the altruistic punishment mechanism was introduced only under the condition of 2 party game. The second chapter of the paper introduced the altruistic punishment mechanism into the N man snow game model of the two strategy for the first time, and established a three strategy N man snow game model with the system of punishing machine. The effect of the introduction of the penalty mechanism on the N man snow pile model in the mixed homogeneous group is investigated. The author gives a series of dynamic equations describing the three strategy model. In the case of sufficient evolution, the system will eventually evolve into a certain steady state, and the steady state is divided into two different characteristics. Generally speaking, a relatively small benefit ratio is given. R, the larger game group size IV, the larger multiplier factor beta / alpha is easy to suppress the breeding of the Betrayer, resulting in the evolution of the system into a cooperative nature, the group composed only by the collaborators and the punishes, because all the betrayals have completed the transformation, the C, the P benefits are completely equal, the system dynamics is frozen, and the steady state is called the frozen state. The frequency composition of the frozen C, P depends on the initial state. On the contrary, the larger R, the smaller IV and the beta / alpha are easy to make the punishing in a self destructive development model, the punishing is gradually disappearing, the system evolves into a group of only collaborators and betrayals, and the Group continues to evolve, equivalent to the original two strategy N man snow pile game model. The dynamic evolution of the C and D frequency composition is independent of the initial state, and it is independent of the parameter setting related to the penalty. The author further proposes a simulation algorithm to fully describe the evolutionary process of the system, which is proved to be in high agreement with the results of the program simulation. In the three chapter, the author studies and establishes a three strategy N man snow pile game model by introducing an additional L strategy in the original two strategy NSG model. The paper derives the dynamic equations of the three strategy frequencies under the mixed homogeneous group structure. Given any initial condition, the time evolution of the frequency can be obtained by the iterative dynamic equation. The different values of the model parameters, the benefit ratio R and the fixed income L, lead to the rich evolutionary behavior of the system. The detailed study of how the display system evolves the trigonometric flow chart shows that the steady state can be one of the AllL, AllC or C + D states based on the model parameter values. The introduction of strategy L has played two roles. It helps to guide the system to the All L state and also to the All C state. In contrast, the introduction of the altruistic punishment mechanism (P strategy) to the N man snow game game can only lead to the steady state of the mixture of two strategies. In addition, the author also uses a simulation algorithm to verify the results of the theoretical study. This algorithm can be used for various structural groups. In the study of NSG model in the fourth chapter, the author increases the lower threshold of a cooperative number based on the optional snow stack game model (Optional NSG). The paper gives the dynamic equation of the model, which is also verified by the simulation algorithm. Similar to the OptionalNSG model, the new model r* also has a critical value r* to make the system a system. The final state of the system is divided into two final steady states. When rr*, the final state of the system is shown as the live dynamic of C and D. When rr*, the final state of the system is the frozen state of ALLL. When the threshold threshold is set to 2, the group finally reaches C, and D coexists positively. But when the lower threshold value continues to increase, it inhibits the cooperation. In the special case of N=T, the Betrayer can never get the benefit by using the collaborator, thus the Betrayer becomes a disadvantaged group. In this context, the system will eventually evolve into two states ALL C and ALL L, and no longer C, D coexists with the end state, to some extent, to change D to C, and eventually eliminate D strategy. In the fifth chapter, the theory On the basis of the OptionalNSG model, the author introduces the punishment mechanism again, and extends the model into a N four strategy game model. The paper gives the dynamic equation of the model, and obtains some preliminary conclusions about the property of the model through the iterative dynamics equation and algorithm, which is similar to the previous model and the four strategy snow of the N man. The heap game model also has a sudden change in the final steady state of a critical value R * expression system. When rr*, with the increase of R, the final state of the system appears as C, P coexists, C, D, P coexist and C, D coexists, and this change is continuous. When rr*, the final state of the system becomes the frozen state of ALLL. This phase transition is transient, and The paper studies the influence of the parameters on the final steady state. It is found that the increase of L makes the key point of transient r* come ahead, the increase of the beta makes the punishment increase, and the increase of N gives the Betrayer the opportunity to use the results of the collaborators, and the difficulty of cooperation is increased.

【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：O225

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