【作者】 李艳；

【导师】 郭万林； 刘心声；

【作者基本信息】 南京航空航天大学 ， 一般力学与力学基础， 2015， 博士

【摘要】 由于广义势函数和广义驱动力的存在,自然界中各种各样的系统,如物理系统、生物系统、化学系统等在平衡和近平衡态附近都可以纳入到一个广泛的统计热力学的理论体系中。这些势和力的存在控制着系统的稳定性和演化方向。合作行为在人类社会、各类生物系统以及金融经济系统等中是普遍存在的。演化动力学为研究由自私理性的个体组成的系统中的合作行为的演化提供了强大且有效的理论方法。当系统中所有个体都合作时,总体的利益可以达到最大,然而就单个个体而言,不劳而获时收益更高。按照达尔文的生物进化论中的优胜劣汰、适者生存法则,适合度低的合作行为会失去进化优势。因此探索自私个体之间的竞争与现实中广泛存在的合作行为之间貌似矛盾实则统一的内在驱动力以及研究各种驱动力对合作进化的影响,是一个重要且具有挑战性的热点课题。本文把所研究的演化博弈系统视为广义力学系统,把影响策略演化的因素或机制看作进化驱动力。进而阐述了复杂网络上的演化博弈,包括网络拓扑结构、个体更新策略的规则等对合作的涌现和演化动力学的影响。针对真实系统中个体相互作用形式的多样性,讨论了多策略博弈的演化动态以及几种驱动力对空间公共品博弈中合作演化的影响。论文主要研究内容及贡献如下:1.利用势函数分析了Wright—Fisher博弈模型的演化动态。在生物系统中,把影响系统进化的驱动力如选择、突变、迁徙等看这种确定性的力,把随机漂变作为随机力。建立了Wright—Fisher博弈模型在不同的驱动力下的势函数,分析了随机力对系统演化的影响。2.研究了空间公共品博弈中持续合作机制对合作进化的影响。在空间公共品博弈中,引入持续合作机制,改进了传统公共品博弈中对总收益的分配方式。持续合作者愿意付出二次代价以获取其贡献出的未平分部分的收益。通过理论分析和数值模拟研究了持续合作策略在具有一维、二维空间结构的总体内的动力学行为,譬如获得系统进化至稳态下的相图,以及在一维网格结构下各策略的固定概率。研究结果表明,相对于均匀混合的总体,持续合作策略在具有空间结构的作用下能更好地抑制背叛策略的传播,促进合作的进化。3.提出了促进传统产业集群内低碳博弈中合作进化的机制。在低碳经济约束下,集群内的企业主体各尽所能,循序渐进地参与低碳化合作。我们基于连续公共品博弈,且充分考虑到各企业主体的异质性,研究了传统产业集群内的低碳化博弈。首先推广了离散策略空间上的持续合作机制,并定义了群体的平均合作水平为评价机制的指标;然后提出了几种利益驱动力:基于博弈小组平均低碳合作水平的多小组均匀投资、多小组非均匀投资以及反映个体投资偏好的非均匀投资。随后研究了这些驱动力对集群的低碳合作化程度的影响。通过对各种驱动力的作用进行数值模拟,结果表明:相对于平均分配投资额度到各个小组的机制,多样化投资和和带偏好的投资方式能更好地提高总体的平均合作水平,尤其是带偏好调节的投资方式。个体投资的偏好性越强,集群的平均低碳化合作水平越高。4.阐明了正则网络上的混合策略的进化稳定性。个体在参与博弈时,未必对博弈环境了如指掌,所以为了在不确定的环境中使得自己的收益最大化,可以采用混合策略博弈。在度为k的图或社会网络上,在弱选择力极限下,本文首先获得了三种策略更新规则(生灭、灭生、模仿)下的两个混合策略相互作用时的收益函数;然后求出各策略更新规则下的连续稳定策略,同时证明了三个连续稳定策略所对应的稳定分布是邻域吸引的和强不可入侵的;最后,将以上所得结果应用到囚徒困境和雪堆博弈中,得到在这两个特殊模型的混合策略博弈中,合作策略受选择青睐的条件,并利用数值模拟验证理论了研究结果的合理性。本论文的研究结果为探索促进公共品博弈中合作的进化提供了新的思路。连续型持续合作机制可用于指导传统产业集群中的低碳化博弈。更多还原

【Abstract】 Various systems including physical systems,biological systems and chemical systems etc can be taken into the framework of generalized statistical thermodynamics due to the extistence of generalized potential function and generalized drives,which determine the stability and evolution of these systems.Cooperation is ubiquitous in human society,various biological systems and economic systems.Evolutionary game theory provides an effective and powerful theoretical framework for investigating the evolution of cooperation in systems consist of selfish and rational individuals.When all the individuals cooperate,the whole population obtains its maximum benefit.However,for any individual,he fares better if he contributes nothing.According to Darwin’s theory of evolution,“survival of the fittest”,cooperation loses its evolutionary superiority owing to its low fitness.Therefore,it is a challenging and significant issue to discover the drive between competition among selfish individuals and omnipresent cooperation behavior,as well as the effects of various drives on the evolution of cooperation.In consideration of the diversity of interactions among individuals in the complex systems,we discuss the impact of some mechanisms proposed in this thesis on the evolution of cooperation in spatial public goods games.The main work and achievements of this dissertation are as follows: 1.The evolutionary of dynamics of Wright—Fisher model is analyzed by potential function.In biological systems,the drives such as selection,mutation and migration are regarded as deterministic forces,while random drift is taken as random force.We first obtain the potential functions under different evolutionary drives,and then we analyze their effects on the evolution of the system.2.The impact of persistent cooperation on the evolutionary of cooperation is discussed in spatial public goods games.A strategy named persistent cooperation is introduced in spatial public goods games,and the way that all the benefit is divided equally among all players in the traditional public goods games is improved.The persistent cooperators will pay a second cost to retrieve the remaining proportion of the total benefit contributed by them.By theoretical analysis and numerical simulations on one-dimensional lattices and square lattices,the evolutionary dynamics of persistent cooperation is obtained,as well as the phase diagram in the stable state for each case.Especially,the fixation probability for each strategy is given on one-dimensional lattice.Comparing to the well-mixed populations,it is found that due to the existence spatial structure-force,persistent cooperators greatly suppresse the spreading of defectors under more relaxed conditions in structured populations.3.The evolution of cooperation is studied in the low-carbon game played in traditional industrial clusters.Under constrains of low-carbon environment,each enterprise pulls his weight to participate the low-carbon economy step by step.Taking the heterogeneity into account,we study the low-carbon game played in the traditional industrial cluster based on the framework of continuous public goods game.We first extend the persistent cooperation mechanism used in discrete strategy space,and define the average level of cooperation in the whole cluster as a measure to the mechanism.Then several mechanisms are developed based on average level of cooperation of the group that an agent belongs to for it to invest in game: even-investment,non-even-investment and preference-investment.Later we study the impacts of different investing mechanisms on the average level of cooperation in low-carbon game.Numerical simulations show that all these investing mechanism can promote the cooperating level.Comparing to even-investment,non-even--investment and preference–investment perform better in promoting the low-carbon cooperation level,especially the preference–investment.The stronger preference an individual has,the higher the average level of cooperation of the whole cluster is.4.The evolutionary stability of mixed-strategy is studied on regular networks of degree k.When facing risk or uncertainty,the assumed rational individuals always expect to maximize their benefit in the game,it would be natural that they play the game with mixed-strategies.Each player is arranged on a vertex of the graph.The edges denote the interactions between two individuals.In the limit of weak selection,we first derive the payoff functions of two mixed-strategies under three different updating rules,named “birth-death”,“death-birth” and “imitation”.Then we obtain the conditions for a strategy being continuously stable strategy(CSS),we also confirm that the equilibrium distribution corresponding to the CSS is neighborhood attracting and strongly uninvadable.Finally we apply our theory to the Prisoner’s Dilemma and the Snow-Drift game to obtain possible CSS.Simulations are performed for the two special games and the results are well consistent with the conclusions we made.The results obtained in this dissertation present a new idea for promoting the evolution of cooperation in public goods games.The continuously persistent cooperation mechanism provides a reference in the low-carbon game played in traditional industrial clusters.更多还原