The different cooperative behaviors on a kind of scale-free networks with identical degree sequence

The power-law degree distribution of scale-free networks plays an important role in the bloom of cooperation in the evolutionary games performed on them. In this paper we apply prisoner’s dilemma and public goods game on a family of scale-free networks with the same degree sequence, and show that power-law behavior alone does not determine the cooperative behavior in scale-free networks. Instead, we present that the direct connections among large-degree nodes have a crucial influence on the evolution of cooperation in the scale-free network family.     

Reputation-based mutual selection rule promotes cooperation in spatial threshold public goods games

Most previous studies involving public goods games are investigated under a simplifying assumption that participation is either compulsive or unidirectional optional in collective interactions. Nevertheless, how the mutual selection rule, a more realistic participation mode, affects the evolution of cooperation in structured populations is still unclear. Here we introduce a reputation-based mutual selection rule for constituting participant groups into spatial threshold public goods games, where the public goods game can be conducted only if the participant number is not less than the threshold parameter. Interestingly, we find that moderate tolerance range results in the best environment for cooperators’ viability. Also, we show that lower member threshold is favorable for the evolution of cooperation, and correspondingly provide some typical snapshots for defectors, “active” cooperators (cooperators on which the public goods games are successfully conducted), and “inactive” cooperators. Moreover, we investigate the effects of memory factor in individuals’ reputation updating on the evolution of cooperation. Our work may provide an appropriate and alternative perspective in understanding the widespread cooperative behaviors in some realistic situations.     

The evolution of cooperation in spatial groups

Much of human cooperation remains an evolutionary riddle. There is evidence that individuals are often organized into groups in many social situations. Inspired by this observation, we propose a simple model of evolutionary public goods games in which individuals are organized into networked groups. Here, nodes in the network represent groups; the edges, connecting the nodes, refer to the interactions between the groups. Individuals establish public goods games with partners in the same group and migrate among neighboring groups depending on their payoffs and expectations. We show that the paradigmatic public goods social dilemma can be resolved and high cooperation levels are attained in structured groups, even in relatively harsh conditions for cooperation. Further, by means of numerical simulations and mean-field analysis, we arrive at the result: larger average group size and milder cooperation environment would lead to lower cooperation level but higher average payoffs of the entire population. Altogether, these results emphasize that our understanding of cooperation can be enhanced by investigations of how spatial groups of individuals affect the evolution dynamics, which might help in explaining the emergence and evolution of cooperation.     

Strategy changing penalty promotes cooperation in spatial prisoner’s dilemma game

Many classical studies suggest that punishment is a useful way to promote cooperation in the well-mixed public goods game, whereas relative evidence in the research of spatial prisoner’s dilemma game is absent. To address this issue, we introduce a mechanism of strategy changing penalty, combining memory and penalty during the update process, into spatial prisoner’s dilemma game. We find that increasing penalty rate or memory length is able to promote the evolution of cooperation monotonously. Compared with traditional version, recorded penalty could facilitate cooperation better. Moreover, through examining the process of evolution, we provide an interpretation for this promotion phenomenon, namely, the effect of promotion can be warranted by an evolution resonance of standard deviation of fitness coefficient. Finally, we validate our results by studying the impact of uncertainty within strategy adoptions on the evolution of cooperation. We hope that our work may shed light on the understanding of the cooperative behavior in the society.     

An improved public goods game model with reputation effect on the spatial lattices

How to model the evolution of cooperation within the population is an important and interdisciplinary issue across the academia. In this paper, we propose an improved public goods game model with reputation effect on spatial lattices to investigate the evolution of cooperation regarding the allocation of public resources. In our model, we modify the individual utility or fitness as a product of the present payoff and reputation-related power function, and strategy update adopts a Fermi-like probability function during the game evolution. Meanwhile, for an interaction between a pair of partners, the reputation of a cooperative agent will be accrued beyond two units, but the defective player will decrease his reputation by one unit. Extensive Monte Carlo numerical simulations indicate the introduction of reputation will foster the formation of cooperative clusters, and greatly enhance the level of public cooperation on the spatial lattices. The larger reputation factor leads to the higher cooperation level since the reputation effect will be enormously embedded into the utility evaluation under this scenario. The current results are vastly beneficial to understand the persistence and emergence of cooperation among many natural, social and synthetic systems, and also provide some useful suggestions to devise the feasible social governance measures and modes for the public resources or affairs.     

演化博弈与自组织合作

主要研究复杂网络上的演化博弈.首先研究具有社团结构的无标度网络上的演化囚徒困境博弈及Newman-Watts小世界网络中异质性对合作演化的影响.然后考察了在不同合作者和作弊者初始分布配置情况下,不同的初始比例条件对合作水平的影响,且在社会网络上研究了雪堆博弈中的合作演化.进一步地,讨论了网络拓扑和博弈动力学的共同演化问题和网络上演化囚徒困境中的强化学习问题.最后给出了复杂网络上演化博弈论的未来发展方向与应用前景.     

Inverse Stackelberg Public Goods Game with Multiple Hierarchies Under Global and Local Information Structures

This paper studies the inverse Stackelberg game with multiple hierarchies under global and local information structures, where the players have discrete strategy spaces. For the classic public goods game, we solve the pure-strategy inverse Stackelberg equilibria under three typical hierarchical structures. The results reveal some counterintuitive characteristics within the systems with hierarchies, such as that the cooperation does not increase with the return rate at the equilibria. Furthermore, by defining a local information structure, we give an estimate of the fewest hierarchies required for full cooperation, which can be a constant multiple of the logarithm or square root of the population size or of the population size itself, according to different information structures and return rates. This paper proposes a novel mechanism to play the game and promote cooperation. Both the formulation and analysis method are different from existing works, and the results can find their ample implications in practice, which might help decision making in hierarchical systems.     

Endogenous formation of networks for local public goods

The paper studies a situation in which agents can make a binding agreement both on the amount of local public goods and on the structure of networks through which they share the benefits of public goods. An agent enjoys the benefit of public goods produced by other agents who are (directly or indirectly) connected to him. There is a cost to maintain a link as well as to produce a public good. Because agents can choose the amount of public goods, the value of a link is endogenously determined. We consider two different models of sequential bargaining games through which a contract on allocations is established. In the first model, we allow agents to propose a pure allocation and show that there is no symmetric stationary perfect equilibrium for sufficiently patient agents. In the second model, agents are allowed to propose a distribution on allocations. As a result, we find a symmetric stationary perfect equilibrium in which probabilistic choices are made on an equivalent class of allocations. Subsequently, we characterize core allocations, which consist of a minimally connected network and an effort profile, in which at most one agent does not produce the maximum amount of public good.     

How behaviors spread in dynamic social networks

In this paper, we explore how decentralized local interactions of autonomous agents in a network relate to collective behaviors. Earlier work in this area has modeled social networks with fixed agent relations. We instead focus on dynamic social networks in which agents can rationally adjust their neighborhoods based on their individual interests. We propose a new connection evaluation theory, the Highest Weighted Reward (HWR) rule: agents dynamically choose their neighbors in order to maximize their own utilities based on rewards from previous interactions. We prove that, in the two-action pure coordination game, our system would stabilize to a clustering state in which all relationships in the network are rewarded with an optimal payoff. Our experiments verify this theory and also reveal additional interesting patterns in the network.     

考虑情感的三策略囚徒困境博弈模型与合作演化

基于社会比较情境下强者和弱者之间产生的同情、欺凌、漠然、尊敬、嫉妒和畏惧等6种情感,建立个体情感特征的定量表达方法。考虑情感驱动的三策略囚徒困境博弈模型,设计了6种情感与合作、背叛及孤独3个博弈策略之间的对应关系和定量表达机制。采用二维格子网络、随机网络和无标度网络等三种网络模型进行演化博弈仿真分析。结果显示:较大的背叛成功诱惑促进了采取背叛策略的情感类型发展演化和繁荣稳定,系统的最终演化状态都体现出程度不同的负性情感特征;空间网络结构对情感类型和合作行为的演化存在重要影响,无标度网络结构能够导致具有一定良性特征的情感类型演化稳定,并带来较高的合作水平;从社会比较及由此产生的对比效应和同化效应的角度,对三种网络下不同的情感演化状态进行了相应阐释。     

Mutual punishment promotes cooperation in the spatial public goods game

Punishment has been proved to be an effective mechanism to sustain cooperation among selfish individuals. In previous studies, punishment is unidirectional: an individual i can punish j but j cannot punish i. In this paper, we propose a mechanism of mutual punishment, in which the two individuals will punish each other if their strategies are different. Because of the symmetry in imposing the punishment, one might expect intuitively the strategy to have little effect on cooperation. Surprisingly, we find that the mutual punishment can promote cooperation in the spatial public goods game. Other pertinent quantities such as the time evolution of cooperator density and the spatial distribution of cooperators and defectors are also investigated.     

利益驱动对创新网络合作行为演化的影响机理及仿真——基于复杂网络拓扑结构视角

随着合作创新的网络化发展,创新网络中各主体的利益诉求对网络演化的影响不断加深。基于不同网络拓扑结构视角下不同利益对创新网络主体合作行为的影响,建立了创新网络演化博弈模型。在无标度与小世界网络拓扑结构下,结合声誉机制、学习行为、网络环境等因素,对创新网络中合作行为的演化进行了仿真研究。结果表明:创新网络的合作行为演化受到网络结构及规模的双重影响,在无标度网络下,合作率更加稳定;合作利益的公平分配促进创新网络合作行为的演化;机会利益的诱惑导致创新网络合作行为的显著波动。     

阈值风险下的多企业合作治理污染的演化博弈分析

针对环境污染具有跨区域性,环境资源的公共物品属性,由单一产污企业治理污染物难以取得有效成果,辖区内多个产污企业合作治理是环境保护的必由之路。 本文从演化博弈论的研究视角探讨了多个排污企业之间的决策演化过程,建立了多主体演化博弈模型,并考虑了污染排放总量超过总量阈值时的环境恶化风险,研究阈值风险对产污企业合作治理污染策略选择的影响。 研究结果表明,较高的治理成本很大地约束了逐利企业治理污染的行为选择,造成公地悲剧的社会问题。 企业治污成本较大背景下,环境阈值风险发生概率越高,越能有效促进合作治理环境策略的演化稳定,合作治理占优于不治理。 出于对企业自身初始禀赋的保护,产污企业初始禀赋越大、排污收费率越高,越能有效促进企业治理污染物的积极性。 最后,为促进辖区内污染企业合作治理污染提出了政策建议。     

Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics

In this paper, we investigate the role of update or imitation rules in the spatial snowdrift game on regular lattices. Three different update rules, including unconditional imitation (UI), replicator dynamics (RD) and the Moran process, are utilized to update the strategies of focal players during the game process in the spatial snowdrift on the lattice. We observe that the aggregate cooperation level between players is largely elevated by using the Moran process in the spatial snowdrift game, when compared to the UI or replicator dynamics. Meanwhile, we carefully explore the dynamical evolution of frequency of cooperators and the cluster formation pattern for these three update rules. Moreover, it is also shown that the evolutionary behavior under the Moran update is independent of and insensitive to the randomly initial configurations of cooperators and defectors. The current results clearly indicate that the introduction of moderate randomness in the strategy update will highly promote the maintenance and persistence of cooperation among selfish individuals, which will be greatly instrumental to deeply understand the evolution of cooperation within many natural, biological and social systems.     

基于社会网络结构的创新扩散动力机制及其仿真研究

随着社会资本的大量涌入,创新扩散逐渐受到社会网络关系的影响。在分析了创新扩散机理的基础上,构建了基于不同拓扑结构的创新扩散演化动力模型。将信息获取、领导者创新能力及机会利益作为创新扩散的动力因子。通过利用复杂网络的演化博弈仿真分析,揭示了小世界、无标度等不同网络拓扑结构下,创新技术的扩散情况。仿真结果表明:在网络结构相同的情况下,信息获取对创新扩散的影响较大;在动力因子设定相同的情况下,网络主体连接越规则,创新扩散越充分。     

基于复杂网络演化博弈的企业低碳创新合作行为网络演化机理研究

针对企业低碳创新合作所面临的复杂问题,基于现实复杂网络结构特征,运用演化博弈理论研究有限理性下企业低碳创新合作行为网络演化机理,利用Matlab仿真技术探究无标度网络载体上微观因素对低碳创新合作行为的影响。研究结果表明:低碳创新利益分配、协同效益和违约惩罚对低碳创新合作行为网络演化结果的影响最为显著,网络规模越大网络演化速度越慢,网络规模越小对协同系数和利益分配系数的敏感性越强,网络规模越大对技术溢出系数和违约惩罚的敏感性越强。研究结论可以为企业低碳创新合作策略制定提供解决依据。     

The influence of random interactions and decision heuristics on norm evolution in social networks

In this paper we explore the effect that random social interactions have on the emergence and evolution of social norms in a simulated population of agents. In our model agents observe the behaviour of others and update their norms based on these observations. An agent’s norm is influenced by both their own fixed social network plus a second random network that is composed of a subset of the remaining population. Random interactions are based on a weighted selection algorithm that uses an individual’s path distance on the network to determine their chance of meeting a stranger. This means that friends-of-friends are more likely to randomly interact with one another than agents with a higher degree of separation. We then contrast the cases where agents make highest utility based rational decisions about which norm to adopt versus using a Markov Decision process that associates a weight with the best choice. Finally we examine the effect that these random interactions have on the evolution of a more complex social norm as it propagates throughout the population. We discover that increasing the frequency and weighting of random interactions results in higher levels of norm convergence and in a quicker time when agents have the choice between two competing alternatives. This can be attributed to more information passing through the population thereby allowing for quicker convergence. When the norm is allowed to evolve we observe both global consensus formation and group splintering depending on the cognitive agent model used.     

Contagion and coordination in random networks

We study the problem of spreading a particular behavior among agents located in a random social network. In each period of time, neighboring agents interact strategically playing a 2 ×  2 coordination game. Assuming myopic best-response dynamics, we show that there exists a threshold for the degree of risk dominance of an action such that below that threshold, contagion of the action occurs. This threshold depends on the connectivity distribution of the network. Based on this, we show that the well-known scale-free networks do not always properly support this type of contagion, which is better accomplished by more intermediate variance networks.     

Enhanced cooperation in prisoner’s dilemma with aspiration

We develop an aspiration-based dynamic model which leads to enhanced cooperation in the Prisoner’s Dilemma game played by the continuous population of agents. The main idea is to limit the aggregate information available to the agents. The model–a system of three nonlinear differential equations–describes the evolution of the aspiration levels of players who use different strategies, and the evolution of the mean frequency of the cooperative strategy in the system of players. The stationary (partial) cooperation level is calculated explicitly. We demonstrate that, contrary to the similar model with only one global aspiration level, the stationary cooperation level can be greater than half.     

乡村振兴战略下农村人居环境整治PPP模式合作行为演化博弈分析

农村人居环境整治是乡村振兴战略的重要内容,基于有限理性的演化博弈理论,构建了以地方政府、社会资本和农村居民为博弈主体的农村人居环境整治PPP模式合作行为演化博弈模型,运用Matlab软件分析了三方主体的初始意愿和政府规制对三方主体行为策略演化的影响。研究发现:(1)政府规制对农村人居环境整治PPP模式合作博弈系统演化的影响从大到小依次是:政府对社会资本的补贴资助、投机罚金、合作奖励和政府对农村居民的参与奖励。(2)与提高地方政府对社会资本的补贴资助力度和惩罚力度相比,提高地方政府的激励规制初始意愿更能促进农村人居环境整治PPP项目的顺利落地实施。(3)农村居民参与PPP项目的初始意愿的提升关键在于提高农村居民参与收益。最后,为促进PPP模式在农村环境治理领域的应用与发展和推动农村人居环境整治的可持续改善提出相应建议。