具资源效应的非对称“鹰鸽博弈”进化稳定分析

解释合作行为的演化一直是生命科学及社会学研究的重要问题之一。经典理论研究大都关注于合作双方对等的情况。然而,在合作系统中的合作双方通常是不对等的,由此可带来博弈双方支付的非对称并影响合作双方的合作行为。该文基于经典的"鹰鸽博弈"模型,同时考虑非对称性相互关系和资源压力的影响,建立了具有强弱之分的四策略(实力强且合作、实力强且不合作、实力弱且合作和实力弱且不合作)非对称博弈模型。结合演化博弈理论及动力系统稳定性理论分析发现:在系统达到稳定状态时,四种策略的比例变化显著地依赖于博弈双方的强弱之比、资源压力及冲突的单位成本收益。对模型的进一步分析显示,当资源充足时,实力强且合作的比例与冲突的单位成本收益负相关;而实力强且不合作、实力弱且不合作的比例都与冲突的单位成本收益正相关,并且随着系统强弱对比增加,实力强且合作及实力强且不合作的比例均增加,而实力弱且不合作的比例将减小。当资源短缺时,模型得出一个有趣的结论,即随着博弈双方的强弱之比的变化,经典的"智猪博弈"与"鹰鸽博弈"可相互转化,该结论将能为不同均衡状态之间的相互转化给出一个动力学解释。     

基于演化博弈视角的环境正义下重工业区工业碳排放治理机制

探寻生态文明建设背景下重工业区工业碳排放治理机制,对于实现“双碳”目标和环境正义具有重要意义。本研究以辽宁重工业区为例,构建地方政府、工业企业和第三方核查机构三方演化博弈模型,探讨影响工业碳排放策略选择的关键因素,对不同均衡点下三方利益主体的策略选择进行仿真,进而构建工业碳排放治理机制。结果表明: 不同均衡情景下,研究区工业碳排放利益主体策略选择分别符合现实和理想两种情景。在三方利益主体博弈的不同均衡情景中,地方政府和第三方核查机构在不同稳定性均衡情景碳排放策略选择中分别起主导作用。政策补贴、违规行为罚款、减排成本、核查成本和监管成本是研究区工业碳排放三方利益主体演化博弈的关键影响因素。结合工业碳排放的关键影响因素,从创新机制、约束机制、市场机制和倒逼机制4个方面构建研究区工业碳排放治理机制。完善研究区工业碳排放利益均衡分配,促进三方利益主体合作,可实现工业碳排放利益主体博弈下的环境正义。     

非对称性有利于合作行为的演化

解释合作行为的演化一直是社会行为学和进化生物学研究的核心问题之一. 经典的亲选择和互惠选择理论认为, 合作双方由于高度的亲缘关系(遗传相似性)或互惠关系而存在合作均衡或进化稳定策略. 这些经典合作演化理论都暗含合作双方是对称的前提假设, 即合作双方的实力对等. 然而, 在现实的合作系统中, 博弈双方几乎都是实力不对等的非对称性相互关系. 运用“鹰鸽博弈”模型及博弈理论发现, 若博弈双方的实力不对等, 博弈双方冲突的频率与博弈双方实力的对比有着密切关系, 即: 博弈双方实力对比越悬殊, 合作的频率越大, 而实力对等时发生冲突的频率最大. 该结果表明, 相互作用个体间的非对称性将可能是合作关系演化的关键动力之一, 且非对称性合作系统并不存在稳定的纯策略Nash均衡. 模型结果有效地解释了为什么在几乎所有的著名合作系统中都观测到了合作双方的冲突行为. 该模型同时发现, 博弈双方发生合作频率的大小与冲突的单位成本收益呈负相关, 而合作方冲突行为的单位成本收益可能取决于合作个体从其系统扩散到其他系统的几率或从原有系统退出的成本大小. 而扩散到其他系统几率越小, 或退出成本越高, 合作接受方(优势方)对合作方的不合作行为惩罚越可信, 合作系统因而可能越稳定.     

活跃连接下Wright-Fisher过程的演化动态

在活跃连接下讨论了2×2对称博弈中频率相依Wright-Fisher过程的演化动力学,得到弱选择下策略的固定概率.利用固定概率讨论囚徒困境与雪堆博弈的演化动态,给出促使合作行为的条件.最后对所得结果进行数值模拟,发现活跃连接可以有效地促进合作行为.     

两个种群随机共进化动态

本文研究同时考虑内外部博弈的两个种群的随机进化动态,博弈的双方个体既可以来自不同种群,也可以来自同一种群,不同种群个体之间的博弈为非对称的,同一种群个体之间的博弈为对称的.我们首先介绍由四个收益矩阵描述的两个种群博弈模型,然后通过突变-选择Moran过程分析了这种随机共进化过程,最后推导出中性选择及弱选择时策略均衡频率的公式.     

一个具有年龄结构的博弈理论模型的研究

考虑一个鹰-鸽博弈的模型.在这个模型里,动物只知道自己的年龄,而不知道对方的年龄.对于这一个博弈模型,将会证明,在进化的平衡点上,存在两个不同的年龄临界点x1和x2(不妨设x1小于x2),并且年龄在这两个临界点之间的动物将会选择鹰策略;而年龄小于x1和年龄大于x2的动物将会选择鸽子策略.在这里,战争发生的可能性大小定义为:当两个个体相遇时,双方都选择鹰策略的概率.进一步,即使动物仅知道自己的年龄,那么在进化稳定性上战争发生的可能性大小也要比标准的鹰-鸽博弈中战争发生的可能性大小要低.     

自然保护区管理的博弈分析

自然保护区作为地球上生态保育的基石,其管理的有效性和可持续性一直是备受关注的热点问题之一。自然保护区管理涉及自然环境和社会经济两大系统,具有复杂性特征。为解析这种复杂性,可以把自然保护区管理看成是博弈问题,将博弈论作为有力工具来解决自然保护区管理中的各种矛盾冲突,协调各种利益关系,以促进自然保护区管理的科学性、有效性和可持续性。一般地,自然保护区可以描述为n人博弈,能够通过Nash均衡和n人合作博弈的Shapley值以及核仁(Nucleolus)等方法求解。作者用博弈论思想分析了自然保护区管理中天然林保护、以电代柴和适度开发等典型案例,总结了自然保护区管理博弈分析的一般步骤。认为必须通过政策、体制和机制创新,促进自然保护区管理中各利益主体的广泛参与和密切合作,才能实现自然保护区管理中公平与效率、高效与持续的统一。     

基于演化博弈的煤炭矿区生态修复管理机制研究

地方政府环境监管部门和煤炭企业是煤炭矿区生态修复保证金制度实施的重要责任主体。从演化博弈论的研究视角探讨了地方政府与煤炭企业在生态修复保证金制度实施中的决策演化过程,构建了地方政府与煤炭企业演化博弈模型,根据复制动态方程规律得到了参与者的行为演化规律和行为演化稳定策略,分析了生态修复保证金制度实施的策略选择影响因素。选择龙口矿区为研究对象进行了实证研究,结果表明:地方政府的监管力度随煤炭企业的生态修复比例变化而变化,生态修复初期比例低;随着地方政府监管力度加大,生态修复比例相应提高,地方政府可以适当放松监管,但监管力度应保持在一定范围内,确保系统向最优状态演化。可通过动态调节保证金收缴金额,增加税收优惠,降低煤炭企业的治理成本,加强对地方政府环保政绩考核,引导地方政府与煤炭企业共同促进煤炭矿区生态修复工作有效实施。     

跨区域森林生态补偿的演化博弈分析——基于主体功能区的视角

新常态下,我国的森林生态环境承载力已经达到或接近上限,森林资源存在乱砍乱伐现象和林区政府监管乏力问题,究其根源是缺乏森林保护和补偿的驱动机制。在中央政府投入大量物力和财力的同时,其他利益相关主体却存在不同利益诉求和行为导向冲突,跨区域森林生态补偿难以实现,因此利用演化博弈模型厘清森林生态环境保护与补偿行动中保护主体、受益主体和中央政府的关系,有助于突破跨区域森林生态保护补偿困境,形成良好的行动机制。分析主体功能区利益群体逻辑关系的基础上,构建保护地区政府和受益地区政府的演化博弈模型,分别研究未引入"约束-激励"机制和引入"约束-激励"机制下的主体行为特征及其影响因素,剖析不同情形地方政府间的博弈决策行为。研究结果表明,在未引入中央政府"约束-激励"机制的情况下,跨区域生态补偿无法实现,保护地区政府会通过权衡保护森林资源收益和机会成本进行策略选择,当保护森林资源的净收益为正时,即使没有受益地区生态补偿,保护地区政府仍然有足够的激励保护森林资源,当保护森林资源的净收益为负时,两类政府群体容易陷入森林生态治理的"囚徒困境",而"约束-激励"机制的引入可以实现森林生态保护补偿的帕累托改进,通过中央政府惩罚、奖励金额的限制能够实现最优稳定均衡策略。     

海洋牧场生态安全监管的演化博弈模型及仿真

海洋牧场生态安全监管是由政府部门对海洋牧场企业的资源开发利用、环境治理保护等行为进行监督和管理，保证海洋牧场海域的资源与环境符合生态安全需要，其对实现海洋牧场的环境保护、资源养护和渔业持续产出功能具有重要作用。首先分析了海洋牧场生态安全监管中的参与主体为政府部门和海洋牧场企业，然后从监管与不监管、重视与不重视两个维度构建了海洋牧场生态安全监管博弈参与主体的策略集合及收益矩阵，在此基础上结合复制动态方程和雅可比矩阵求解了海洋牧场生态安全监管博弈中演化稳定策略并进行了稳定性分析和模拟仿真，最后提出了海洋牧场生态安全监管的对策建议。研究结果表明，对海洋牧场企业不重视生态安全行为的惩罚力度、政府部门从发现企业不重视生态安全中获取的收益、外界监督力量监督成功的概率是影响演化博弈结果的重要因素。据此提出"加大对海洋牧场企业不重视海洋牧场生态安全行为的处罚力度、提高政府部门发现海洋牧场企业不重视海洋牧场生态安全时的收益、建立健全海洋牧场生态安全监管机制、发挥外界监督力量的作用"等政策建议，以维护我国海洋牧场生态安全。     

Asymmetric interaction will facilitate the evolution of cooperation

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. However, the payoff between partners is usually not equal and therefore they often interact asymmetrically in real cooperative systems. With the Hawk-Dove model, we find that the probability of cooperation between cooperative partners will depend closely on the payoff ratio. The higher the payoff ratio between recipients and cooperative actors, the greater will be the probability of cooperation interaction between involved partners. The greatest probability of conflict between cooperative partners will occur when the payoff between partners is equal. The results show that this asymmetric relationship is one of the key dynamics of the evolution of cooperation, and that pure cooperation strategy (i.e., Nash equilibrium) does not exist in asymmetrical cooperation systems, which well explains the direct conflict observed in almost all of the well documented cooperation systems. The model developed here shows that the cost-to-benefit ratio of cooperation is also negatively correlated with the probability of cooperation interaction. A smaller cost-to-benefit ratio of cooperation might be created by the limited dispersal ability or exit cost of the partners involved, and it will make the punishment of the non-cooperative individuals by the recipient more credible, and therefore make it more possible to maintain stable cooperation interaction.     

Evolution of cooperation with shared costs and benefits

The quest to determine how cooperation evolves can be based on evolutionary game theory, in spite of the fact that evolutionarily stable strategies (ESS) for most non-zero-sum games are not cooperative. We analyse the evolution of cooperation for a family of evolutionary games involving shared costs and benefits with a continuum of strategies from non-cooperation to total cooperation. This cost-benefit game allows the cooperator to share in the benefit of a cooperative act, and the recipient to be burdened with a share of the cooperator's cost. The cost-benefit game encompasses the Prisoner's Dilemma, Snowdrift game and Partial Altruism. The models produce ESS solutions of total cooperation, partial cooperation, non-cooperation and coexistence between cooperation and non-cooperation. Cooperation emerges from an interplay between the nonlinearities in the cost and benefit functions. If benefits increase at a decelerating rate and costs increase at an accelerating rate with the degree of cooperation, then the ESS has an intermediate level of cooperation. The game also exhibits non-ESS points such as unstable minima, convergent-stable minima and unstable maxima. The emergence of cooperative behaviour in this game represents enlightened self-interest, whereas non-cooperative solutions illustrate the Tragedy of the Commons. Games having either a stable maximum or a stable minimum have the property that small changes in the incentive structure (model parameter values) or culture (starting frequencies of strategies) result in correspondingly small changes in the degree of cooperation. Conversely, with unstable maxima or unstable minima, small changes in the incentive structure or culture can result in a switch from non-cooperation to total cooperation (and vice versa). These solutions identify when human or animal societies have the potential for cooperation and whether cooperation is robust or fragile.     

城市扩张与水污染物排放的伴生效应与交互机理——基于2011-2015年长三角地区的实证检验

揭示城市扩张与水污染物排放之间的伴生效应与空间交互机理是城市化水环境效应研究的重要议题。以长三角地区为例,选取COD和NH₃-N两项特征污染物指标,在2011—2015年快速城市化时期的水污染物排放格局分析基础上,优选空间杜宾模型估计城市扩张与水污染物排放的伴生效应,采用直接效应和间接效应分解定量测度二者的空间交互机理。研究结果表明：2011—2015年长三角地区水污染物排放规模显著下降,县域排放强度等级整体降低,高强度排放格局由连片式分布收缩为零散式分布;城市扩张与水污染物排放的伴生效应显著而稳定,高扩张-高排放型县域在上海及其周边、苏北地区集中分布,沿海和沿江区位是城市扩张通常会选择的布局指向,在排污距离成本和环境规制强度双重作用下,距海岸线和长江干流距离越远,水污染物排放强度越呈对数曲线式降低;城市扩张与水污染物排放的空间交互作用具有两面性,城市扩张规模每提升1%,使本地COD、NH₃-N排放分别增加0.274%、0.368%的同时,还会造成邻近县域排放降低1.017%、0.650%。因此,为缓解城市扩张与水污染物排放的伴生效应和交互作...     

Interactions between personality and institutions in cooperative behaviour in humans

Laboratory attempts to identify relationships between personality and cooperative behaviour in humans have generated inconsistent results. This may partially stem from different practices in psychology and economics laboratories, with both hypothetical players and incentives typical only in the former. Another possible cause is insufficient consideration of the contexts within which social dilemmas occur. Real social dilemmas are often governed by institutions that change the payoff structure via rewards and punishments. However, such ‘strong situations’ will not necessarily suppress the effects of personality. On the contrary, they may affect some personalities differentially. Extraversion and neuroticism, reflecting variation in reward and punishment sensitivity, should predict modification of cooperative behaviour following changes to the payoff structure. We investigate interactions between personality and a punishment situation via two versions of a public goods game. We find that, even in a strong situation, personality matters and, moreover, it is related to strategic shifts in cooperation. Extraversion is associated with a shift from free-riding to cooperation in the presence of punishment, agreeableness is associated with initially higher contributions regardless of game, and, contrary to our predictions, neuroticism is associated with lower contributions regardless of game. Results should lead to new hypotheses that relate variation in biological functioning to individual differences in cooperative behaviour and that consider three-way interactions among personality, institutional context and sociocultural background.     

How strategy environment and wealth shape altruistic behaviour: cooperation rules affecting wealth distribution in dynamic networks

Societies rely on individual contributions to sustain public goods that benefit the entire community. Several mechanisms, that specify how individuals change their decisions based on past experiences, have been proposed to explain how altruists are not outcompeted by selfish counterparts. A key aspect of such strategy updates involves a comparison of an individual''s latest payoff with that of a random neighbour. In reality, both the economic and social milieu often shapes cooperative behaviour. We propose a new decision heuristic, where the propensity of an individual to cooperate depends on the local strategy environment in which she is embedded as well as her wealth relative to that of her neighbours. Our decision-making model allows cooperation to be sustained and also explains the results of recent experiments on social dilemmas in dynamic networks. Final cooperation levels depend only on the extent to which the strategy environment influences altruistic behaviour but are largely unaffected by network restructuring. However, the extent of wealth inequality in the community is affected by a subtle interplay between the environmental influence on a person''s decision to contribute and the likelihood of reshaping social ties, with wealth-inequality levels rising with increasing likelihood of network restructuring in some situations.     

Cooperative Emissions Trading Game: International Permit Market Dominated by Buyers

Rapid reduction of anthropogenic greenhouse gas emissions is required to mitigate disastrous impacts of climate change. The Kyoto Protocol introduced international emissions trading (IET) to accelerate the reduction of carbon dioxide (CO₂) emissions. The IET controls CO₂ emissions through the allocation of marketable emission permits to sovereign countries. The costs for acquiring additional permits provide buyers with an incentive to reduce their CO₂ emissions. However, permit price has declined to a low level during the first commitment period (CP1). The downward trend in permit price is attributed to deficiencies of the Kyoto Protocol: weak compliance enforcement, the generous allocation of permits to transition economies (hot air), and the withdrawal of the US. These deficiencies created a buyer’s market dominated by price-making buyers. In this paper, I develop a coalitional game of the IET, and demonstrate that permit buyers have dominant bargaining power. In my model, called cooperative emissions trading (CET) game, a buyer purchases permits from sellers only if the buyer forms a coalition with the sellers. Permit price is determined by bargaining among the coalition members. I evaluated the demand-side and supply-side bargaining power (DBP and SBP) using Shapley value, and obtained the following results: (1) Permit price is given by the product of the buyer’s willingness-to-pay and the SBP (= 1 − DBP). (2) The DBP is greater than or equal to the SBP. These results indicate that buyers can suppress permit price to low levels through bargaining. The deficiencies of the Kyoto Protocol enhance the DBP, and contribute to the demand-side dominance in the international permit market.     

Defecting or not defecting: how to "read" human behavior during cooperative games by EEG measurements

Understanding the neural mechanisms responsible for human social interactions is difficult, since the brain activities of two or more individuals have to be examined simultaneously and correlated with the observed social patterns. We introduce the concept of hyper-brain network, a connectivity pattern representing at once the information flow among the cortical regions of a single brain as well as the relations among the areas of two distinct brains. Graph analysis of hyper-brain networks constructed from the EEG scanning of 26 couples of individuals playing the Iterated Prisoner's Dilemma reveals the possibility to predict non-cooperative interactions during the decision-making phase. The hyper-brain networks of two-defector couples have significantly less inter-brain links and overall higher modularity--i.e., the tendency to form two separate subgraphs--than couples playing cooperative or tit-for-tat strategies. The decision to defect can be "read" in advance by evaluating the changes of connectivity pattern in the hyper-brain network.     

Fixation probabilities of random mutants under frequency dependent selection

Evolutionary game dynamics describes frequency dependent selection in asexual, haploid populations. It typically considers predefined strategies and fixed payoff matrices. Mutations occur between these known types only. Here, we consider a situation in which a mutation has produced an entirely new type which is characterized by a random payoff matrix that does not change during the fixation or extinction of the mutant. Based on the probability distribution underlying the payoff values, we address the fixation probability of the new mutant. It turns out that for weak selection, only the first moments of the distribution matter. For strong selection, the probability that a new payoff entry is larger than the wild type's payoff against itself is the crucial quantity.     

Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.