Emergence of cooperation and evolutionary stability in finite populations

To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the 'Prisoner's Dilemma', in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like 'tit-for-tat' can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.     

Human cooperation: second-order free-riding problem solved?

Panchanathan and Boyd describe a model of indirect reciprocity in which mutual aid among cooperators can promote large-scale human cooperation without succumbing to a second-order free-riding problem (whereby individuals receive but do not give aid). However, the model does not include second-order free riders as one of the possible behavioural types. Here I present a simplified version of their model to demonstrate how cooperation unravels if second-round defectors enter the population, and this shows that the free-riding problem remains unsolved.     

Universal role of migration in the evolution of cooperation

We study the role of unbiased migration in cooperation in the framework of the spatial evolutionary game on a variety of spatial structures, namely a regular lattice, continuous plane and complex networks. A striking finding is that migration plays a universal role in cooperation, regardless of the spatial structure. For a high degree of migration, cooperators cannot survive owing to their failure to form cooperator clusters that resist attacks by defectors. Meanwhile, for a low degree of migration, cooperation is considerably enhanced relative to that in the static spatial game, which is due to the strengthening of the boundaries of cooperator clusters by the occasional accumulation of cooperators along the boundaries. The cooperator cluster thus becomes more robust than that in the static game and defectors near the boundary can be assimilated by cooperators. The cooperator cluster thus expands, which facilitates cooperation. The general role of migration will be substantiated by sufficient simulations relating to heuristic explanations.     

人类的迁徙行为与社群合作之演化

通过空间结构(规则格子、连续平面和复杂网络)框架中的空间演化博弈研究,揭示无偏向的迁徙行为对于合作究竟起何作用.研究发现:迁移对于合作起一种普遍的作用,无论其空间结构如何.如果迁徙得太快,合作者将由于无法形成抵抗背叛者攻击的合作者簇团而难于生存.但若迁徙得慢一些,则与无迁徙静态的空间博弈比较,合作将显著强化,这是由于合作者沿着合作者簇团边界的随时加入积累而使得合作者簇团边界趋于硬厚坚固.在迁徙速度适中的情况下,合作者簇团之边界变得比无迁徙静态情况下更为牢固,边界附近的背叛者可以被合作者吸收同化,从而使合作者簇团膨胀,这又使得合作更加方便.同时还特别研究了引入满意度控制的迁徙对于合作演化所起的作用,用广泛的模拟加启发式的解释来证实迁徙所起的普遍性的作用.     

A simple rule for the evolution of cooperation on graphs and social networks

A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals. Human society is based to a large extent on mechanisms that promote cooperation. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity.     

复杂网络上博弈行为演化的合作激励

通过引入人类社会组织的激励机制,研究网络初始状态存在少量合作者时的囚徒困境博弈行为演化,着重探讨激励机制在网络结构作用条件下对群体合作行为产生的影响.首先从理论层面分析当方格网上存在一个合作者时,合作行为演化形成合作者聚集结构的激励条件;然后采用仿真实验方法研究方格网、规则小世界网络和异质小世界网络上随机分布少量合作者时,激励机制对合作行为演化的影响.研究发现,激励机制在不同的网络结构上总体表现出对合作行为演化的促进作用.但是在方格网和规则小世界网络上,由于节点度的同质化效应,针对合作行为的激励有时不一定会产生更好的合作状态,甚至可能起到负面的效果.     

小世界网络中的公共物品博弈

研究了小世界网络中的公共物品博弈,分析了噪声以及网络节点的异质性对博弈行为的影响．我们发现,网络的小世界特性以及网络中的噪声对博弈过程中合作的涌现起抑制作用,而网络节点的异质性则对博弈过程中合作的涌现起促进作用．我们用平均场理论对得到的数值模拟的结果进行了对比和分析．     

合作进化模型综述

作者综述了合作进化模型的最新研究成果。合作进化模型以“囚徒困境”博弈模型为基础, 为合作中的个体提供了一种与个体本身无关的策略优化机制, 以此探讨合作策略能够稳定进化的条件。基于直接或间接互惠理论的合作进化模型验证了在小规模社会中建立声誉机制有助于实现稳定的互惠合作; 互惠可以看做是对合作行为的奖赏, 开放的社会网络有助于实现较大范围内的合作; 对非合作行为实施惩罚有助于实现多人合作, 在一定条件下, 由非合作者实施惩罚时的合作进化相较于由合作者实施时更稳定; 群组竞争有利于合作文化或制度的传播, 但无法解释群组融合后的合作问题。     

Evolution and maintenance of cooperation via inheritance of neighborhood relationship

Cooperative behaviors are ubiquitous in nature and human society. It is very important to understand the internal mechanism of emergence and maintenance of cooperation. As we know now, the offsprings inherit not only the phenotype but also the neighborhood relationship of their parents. Some recent research results show that the interactions among individuals facilitate survival of cooperation through network reciprocity of clustering cooperators. This paper aims at introducing an inheritance mechanism of neighborhood relationship to explore the evolution of cooperation. In detail, a mathematical model is proposed to characterize the evolutionary process with the above inheritance mechanism. Theoretical analysis and numerical simulations indicate that high-level cooperation can emerge and be maintained for a wide variety of cost-to-benefit ratios, even if mutation happens during the evolving process.     

Altruistic punishment in humans.

Human cooperation is an evolutionary puzzle. Unlike other creatures, people frequently cooperate with genetically unrelated strangers, often in large groups, with people they will never meet again, and when reputation gains are small or absent. These patterns of cooperation cannot be explained by the nepotistic motives associated with the evolutionary theory of kin selection and the selfish motives associated with signalling theory or the theory of reciprocal altruism. Here we show experimentally that the altruistic punishment of defectors is a key motive for the explanation of cooperation. Altruistic punishment means that individuals punish, although the punishment is costly for them and yields no material gain. We show that cooperation flourishes if altruistic punishment is possible, and breaks down if it is ruled out. The evidence indicates that negative emotions towards defectors are the proximate mechanism behind altruistic punishment. These results suggest that future study of the evolution of human cooperation should include a strong focus on explaining altruistic punishment.     

Influence of strategy continuity on cooperation in spatial prisoner’s dilemma games with migrating players

The phenomenon of cooperation is prevalent in both nature and human society. In this paper a simulative model is developed to examine how the strategy continuity influences cooperation in the spatial prisoner’s games in which the players migrate through the success-driven migration mechanism. Numerical simulations illustrate that the strategy continuity promotes cooperation at a low rate of migration, while impeding cooperation when the migration rate is higher. The influence of strategy continuity is also dependent on the game types. Through a more dynamic analysis, the different effects of the strategy continuity at low and high rates of migration are explained by the formation, expansion, and extinction of the self-assembled clusters of “partial- cooperators” within the gaming population.     

Reputation helps solve the 'tragedy of the commons'.

The problem of sustaining a public resource that everybody is free to overuse-the 'tragedy of the commons'-emerges in many social dilemmas, such as our inability to sustain the global climate. Public goods experiments, which are used to study this type of problem, usually confirm that the collective benefit will not be produced. Because individuals and countries often participate in several social games simultaneously, the interaction of these games may provide a sophisticated way by which to maintain the public resource. Indirect reciprocity, 'give and you shall receive', is built on reputation and can sustain a high level of cooperation, as shown by game theorists. Here we show, through alternating rounds of public goods and indirect reciprocity games, that the need to maintain reputation for indirect reciprocity maintains contributions to the public good at an unexpectedly high level. But if rounds of indirect reciprocation are not expected, then contributions to the public good drop quickly to zero. Alternating the games leads to higher profits for all players. As reputation may be a currency that is valid in many social games, our approach could be used to test social dilemmas for their solubility.     

考虑车辆间博弈行为的交通流

从二维城市道路元胞自动机交通流模型和一维道路元胞自动机模型两个方面介绍车辆间博弈行为对交通流的影响.总结了目前交通流研究中引入合作者和背叛者之后,道路交通状况的改变.通过考虑车辆之间的博弈行为,研究司机驾驶行为对道路上车流量的影响,希望找到能使交通系统车流量达到最大的驾驶行为准则.     

Social diversity promotes the emergence of cooperation in public goods games

Humans often cooperate in public goods games and situations ranging from family issues to global warming. However, evolutionary game theory predicts that the temptation to forgo the public good mostly wins over collective cooperative action, and this is often also seen in economic experiments. Here we show how social diversity provides an escape from this apparent paradox. Up to now, individuals have been treated as equivalent in all respects, in sharp contrast with real-life situations, where diversity is ubiquitous. We introduce social diversity by means of heterogeneous graphs and show that cooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. When social ties follow a scale-free distribution, cooperation is enhanced whenever all individuals are expected to contribute a fixed amount irrespective of the plethora of public goods games in which they engage. Our results may help to explain the emergence of cooperation in the absence of mechanisms based on individual reputation and punishment. Combining social diversity with reputation and punishment will provide instrumental clues on the self-organization of social communities and their economical implications.     

Self-destructive cooperation mediated by phenotypic noise

In many biological examples of cooperation, individuals that cooperate cannot benefit from the resulting public good. This is especially clear in cases of self-destructive cooperation, where individuals die when helping others. If self-destructive cooperation is genetically encoded, these genes can only be maintained if they are expressed by just a fraction of their carriers, whereas the other fraction benefits from the public good. One mechanism that can mediate this differentiation into two phenotypically different sub-populations is phenotypic noise. Here we show that noisy expression of self-destructive cooperation can evolve if individuals that have a higher probability for self-destruction have, on average, access to larger public goods. This situation, which we refer to as assortment, can arise if the environment is spatially structured. These results provide a new perspective on the significance of phenotypic noise in bacterial pathogenesis: it might promote the formation of cooperative sub-populations that die while preparing the ground for a successful infection. We show experimentally that this model captures essential features of Salmonella typhimurium pathogenesis. We conclude that noisily expressed self-destructive cooperative actions can evolve under conditions of assortment, that self-destructive cooperation is a plausible biological function of phenotypic noise, and that self-destructive cooperation mediated by phenotypic noise could be important in bacterial pathogenesis.     

妇女小组的情感支持功能

家庭暴力作为一种较普遍的社会现象已引起社会的广泛关注。在家庭暴力中绝大多数受害者是女性。女性难以走出暴力困境的主要原因是缺少社会支持，而妇女小组可以为他们提供情感方面的支持。妇女小组的这一功能是通过协作者的态度、小组安排的内容和所采取的方式等来实现的。     

基于博弈分析的图书馆资源共享研究

图书馆是社会中最大形式的公用物品。阐述了公用物品的特征以及反映在公用物品上的博弈问题,探讨了实现公用图书馆投资多元化的措施,分析了基于博弈理论的联合采购及文献共享,指出图书馆实现资源共享的目标需要多方的努力和配合,需要广大读者及社会的支持。     

国民待遇:农村公共产品供给与农民权益保护

全面取消农业税后,在部分地区的农村公共产品的供给中仍然存在着向农民集资、摊派等侵害农民权益的现象.这些现象在实质上是,农民作为平等的国家公民,在公共产品的供给中并没有享受到平等的国民待遇.导致这种状况的根本原因在于,建国后我国选择的重工业优先发展战略以及由此形成的城乡二元的公共产品供给结构.在公共产品的供给上,要给予农民以真正的国民待遇,维护农民权益,从国家的角度讲,最重要的就是要统筹城乡发展,健全公共财政体制;从农民的角度讲,应提高组织化水平,维护自己的利益.     

Social networks and cooperation in hunter-gatherers

Social networks show striking structural regularities, and both theory and evidence suggest that networks may have facilitated the development of large-scale cooperation in humans. Here, we characterize the social networks of the Hadza, a population of hunter-gatherers in Tanzania. We show that Hadza networks have important properties also seen in modernized social networks, including a skewed degree distribution, degree assortativity, transitivity, reciprocity, geographic decay and homophily. We demonstrate that Hadza camps exhibit high between-group and low within-group variation in public goods game donations. Network ties are also more likely between people who give the same amount, and the similarity in cooperative behaviour extends up to two degrees of separation. Social distance appears to be as important as genetic relatedness and physical proximity in explaining assortativity in cooperation. Our results suggest that certain elements of social network structure may have been present at an early point in human history. Also, early humans may have formed ties with both kin and non-kin, based in part on their tendency to cooperate. Social networks may thus have contributed to the emergence of cooperation.     

Maintenance of cooperation in a public goods game: A new decision-making criterion with incomplete information

Hardin’s "The Tragedy of the Commons" prophesies the inescapable collapse of many human enterprises.The emergence and abundance of cooperation in animal and human societies is a challenging puzzle to evolutionary theory.In this work,we introduce a new decision-making criterion into a voluntary public goods game with incomplete information and choose successful strategies according to previous payoffs for a certain strategy as well as the risk-averse benefit.We find that the interest rate of the common pool and the magnitude of memory have crucial effects on the average welfare of the population.The appropriate sense of individuals’ innovation also substantially influences the equilibrium strategies distribution in the long run.