本文選題：囚徒困境 + 合作　； 參考：《清華大學(xué)》2015年碩士論文

【摘要】：囚徒困境(Prisoner's Dilemma)反映了現(xiàn)實(shí)社會(huì)中的諸多社會(huì)問題,其合作行為的出現(xiàn)有利于解決社會(huì)困境。但傳統(tǒng)博弈理論認(rèn)為,理性人只會(huì)選擇非合作行為。合作行為的出現(xiàn)機(jī)理仍然不是很清楚,特別是博弈中合作行為出現(xiàn)的幾率有時(shí)高有時(shí)低。專家學(xué)者呼吁人們應(yīng)該合作以達(dá)到共贏目的,但是缺乏合理有效的機(jī)制設(shè)計(jì),呼吁往往達(dá)不到效果�，F(xiàn)今研究囚徒困境合作概率的模型很少,要提高人們選擇合作的概率,需要從定量的角度分析各種影響因素,才能有依據(jù)地進(jìn)行最優(yōu)機(jī)制設(shè)計(jì)。本文將研究囚徒困境的合作概率,建立數(shù)學(xué)模型,為機(jī)制設(shè)計(jì)的優(yōu)化提供量化分析�？紤]到利益是影響參與者決策的最根本因素,論文首次將囚徒困境收益矩陣中的具體收益直接與合作概率進(jìn)行相關(guān)性分析,得出各收益值與合作概率的正負(fù)相關(guān)性,并進(jìn)一步研究了各收益值對(duì)合作策略的影響程度。論文綜合考慮了收益影響、參與者的決策動(dòng)機(jī)和個(gè)體差異、博弈的相互性等因素,構(gòu)建了囚徒困境合作概率模型,并利用Butler(2012)提供的大量實(shí)驗(yàn)數(shù)據(jù),通過非線性回歸分析等統(tǒng)計(jì)手段,檢驗(yàn)擬合優(yōu)度的大小,驗(yàn)證了概率模型的正確性,完善了囚徒困境的理論研究。模型簡(jiǎn)潔靈活,符合人的決策特點(diǎn)和思考能力。此外論文針對(duì)集體理性(team reasoning,解釋囚徒困境合作行為的動(dòng)機(jī)因素之一)開展概率模型研究。所謂集體理性,指的是人們?cè)谧鰶Q策時(shí)考慮的是集體的利益,而不是個(gè)人利益。本文基于Smerilli(2012)提出的集體理性概率模型,進(jìn)行了模型的補(bǔ)充完善,提出了轉(zhuǎn)移模型的具體函數(shù)形式,由此推導(dǎo)出完整的局中人選擇集體理性的概率公式,并將模型應(yīng)用于利益分配機(jī)制設(shè)計(jì)。具體涉及線性轉(zhuǎn)移模型的構(gòu)建,分析集體理性概率最大化的收益分配方式,進(jìn)而研究擴(kuò)展至非線性轉(zhuǎn)移模型,得出轉(zhuǎn)移模型為凹函數(shù)或凸函數(shù)時(shí)的分配機(jī)制設(shè)計(jì),并予以數(shù)學(xué)證明等。論文還利用了相關(guān)對(duì)稱博弈和非對(duì)稱博弈的系列實(shí)驗(yàn),通過行為實(shí)驗(yàn)對(duì)集體理性概率模型進(jìn)行了驗(yàn)證。
[Abstract]:Prisoner Dilemma (PrisonersDilemma) reflects many social problems in real society, and its cooperative behavior is helpful to solve the social dilemma.But the traditional game theory holds that rational people only choose non-cooperative behavior.The mechanism of cooperative behavior is still unclear, especially the probability of cooperative behavior in games is sometimes high and sometimes low.Experts and scholars call for cooperation to achieve win-win goals, but the lack of reasonable and effective mechanism design, appeals often fail to achieve results.Nowadays, there are few models to study the probability of prisoners' Dilemma cooperation. In order to improve the probability of cooperation, it is necessary to analyze all kinds of influencing factors from a quantitative point of view, in order to design the optimal mechanism according to the basis.In this paper, the cooperative probability of prisoner's dilemma is studied, and the mathematical model is established to provide quantitative analysis for the optimization of mechanism design.Considering that interest is the most fundamental factor that affects the decision of participants, the paper analyzes the correlation between the concrete benefit and the cooperation probability directly in the prisoner's Dilemma income matrix for the first time, and obtains the positive and negative correlation between the benefit value and the cooperation probability.Furthermore, the influence of each profit value on the cooperation strategy is further studied.Considering the influence of income, the decision motivation and individual difference of the participants, and the interaction of game, the paper constructs the probability model of prisoners' Dilemma cooperation, and makes use of a large number of experimental data provided by Butlers2012).By means of statistical means such as nonlinear regression analysis, the size of goodness of fit is tested, the correctness of probability model is verified, and the theoretical study of prisoner's dilemma is perfected.The model is simple and flexible, in line with people's decision-making characteristics and thinking ability.In addition, probabilistic model research is carried out to explain one of the motivational factors of prisoners' Dilemma cooperation behavior.Collective rationality refers to the collective interests, not the individual interests, when people make decisions.Based on the probability model of collective rationality put forward by Smerillier 2012, the model is supplemented and perfected, and the concrete function form of the transfer model is put forward, from which the complete probability formula of selecting collective rationality is derived.The model is applied to the design of benefit distribution mechanism.It involves the construction of the linear transfer model, the analysis of the income distribution mode of maximizing the probability of collective rationality, and the extension to the nonlinear transfer model, and the design of the assignment mechanism when the transfer model is concave function or convex function.And give mathematical proof, etc.A series of experiments of correlation symmetric game and asymmetric game are used to verify the probability model of collective rationality through behavior experiments.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：F224.32

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