囚徒困境合作概率研究

发布时间：2018-04-14 12:42

本文选题：囚徒困境 + 合作　；参考：《清华大学》2015年硕士论文

【摘要】：囚徒困境(Prisoner's Dilemma)反映了现实社会中的诸多社会问题,其合作行为的出现有利于解决社会困境。但传统博弈理论认为,理性人只会选择非合作行为。合作行为的出现机理仍然不是很清楚,特别是博弈中合作行为出现的几率有时高有时低。专家学者呼吁人们应该合作以达到共赢目的,但是缺乏合理有效的机制设计,呼吁往往达不到效果。现今研究囚徒困境合作概率的模型很少,要提高人们选择合作的概率,需要从定量的角度分析各种影响因素,才能有依据地进行最优机制设计。本文将研究囚徒困境的合作概率,建立数学模型,为机制设计的优化提供量化分析。考虑到利益是影响参与者决策的最根本因素,论文首次将囚徒困境收益矩阵中的具体收益直接与合作概率进行相关性分析,得出各收益值与合作概率的正负相关性,并进一步研究了各收益值对合作策略的影响程度。论文综合考虑了收益影响、参与者的决策动机和个体差异、博弈的相互性等因素,构建了囚徒困境合作概率模型,并利用Butler(2012)提供的大量实验数据,通过非线性回归分析等统计手段,检验拟合优度的大小,验证了概率模型的正确性,完善了囚徒困境的理论研究。模型简洁灵活,符合人的决策特点和思考能力。此外论文针对集体理性(team reasoning,解释囚徒困境合作行为的动机因素之一)开展概率模型研究。所谓集体理性,指的是人们在做决策时考虑的是集体的利益,而不是个人利益。本文基于Smerilli(2012)提出的集体理性概率模型,进行了模型的补充完善,提出了转移模型的具体函数形式,由此推导出完整的局中人选择集体理性的概率公式,并将模型应用于利益分配机制设计。具体涉及线性转移模型的构建,分析集体理性概率最大化的收益分配方式,进而研究扩展至非线性转移模型,得出转移模型为凹函数或凸函数时的分配机制设计,并予以数学证明等。论文还利用了相关对称博弈和非对称博弈的系列实验,通过行为实验对集体理性概率模型进行了验证。
[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.
【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F224.32

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