社会困境下双重度偏好社团网络合作涌现研究
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摘要
考虑复杂社会网络中的"社团结构"特征,基于经典的囚徒困境博弈和累积收益策略更新规则,构建社会困境下具有双重度偏好的社团网络演化博弈模型,系统研究静态社团网络外部连接密度、动态社团网络中策略与结构共演化时间尺度以及策略更新中噪声对合作涌现的影响及其作用机理。研究发现,社团网络间连接密度对合作涌现具有负向影响;尽管静态社团网络合作水平在数值上是明显高于动态社团网络,但其合作演化的策略构成、策略稳定性及其演化动态性存在显著差异;动态社团网络中策略与结构共演化的时间尺度对合作涌现的影响呈现相对优劣互转的变化趋势,具体表现为在低背叛诱惑值下时间尺度越小越不利于合作,而在高背叛诱惑值下时间尺度越小越有利于合作;策略更新过程中噪声对静态和动态社团网络合作涌现的影响是单调的,且适度的引入噪声能够显著提高合作水平。
According to the community structure in complex social networks, we propose an evolutionary game model on community network generated by the double-degree preference mechanism under social dilemma, based on traditional Prisoner's Dilemma Game and accumulated payoff update rule. Then, we systematically analyze the effect of external connectivity density in static community networks, co-evolution time scale of strategy and structure in dynamic community network, and the noise in updating process on the emergence of cooperation and the corresponding mechanism. The results of simulation indicate that: the density of connections between communities has a negative impact on the emergence of cooperation. Although the level of cooperation in static community networks is higher than dynamic community networks, there are significant differences between static and dynamic community networks for the strategy composition, strategy stability and dynamics of cooperative evolution. In dynamic community networks, the effect of co-evolution time scale of strategy and structure on cooperation emergence shows reciprocal trend of change between pros and cons, which represents that it has a smaller cooperation level with smaller time scale under low value of temptation while it is more beneficial for cooperation with smaller time scale under high value of temptation. The effect of noise in strategy updating process on the cooperation emergence in static and dynamic community networks is monotonous, and it can significantly increases the cooperation level by introducing moderate noise.
According to the community structure in complex social networks, we propose an evolutionary game model on community network generated by the double-degree preference mechanism under social dilemma, based on traditional Prisoner's Dilemma Game and accumulated payoff update rule. Then, we systematically analyze the effect of external connectivity density in static community networks, co-evolution time scale of strategy and structure in dynamic community network, and the noise in updating process on the emergence of cooperation and the corresponding mechanism. The results of simulation indicate that: the density of connections between communities has a negative impact on the emergence of cooperation. Although the level of cooperation in static community networks is higher than dynamic community networks, there are significant differences between static and dynamic community networks for the strategy composition, strategy stability and dynamics of cooperative evolution. In dynamic community networks, the effect of co-evolution time scale of strategy and structure on cooperation emergence shows reciprocal trend of change between pros and cons, which represents that it has a smaller cooperation level with smaller time scale under low value of temptation while it is more beneficial for cooperation with smaller time scale under high value of temptation. The effect of noise in strategy updating process on the cooperation emergence in static and dynamic community networks is monotonous, and it can significantly increases the cooperation level by introducing moderate noise.
引文
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[2]VANLANGE P A M,BALLIET D P,PARKS C D.Social dilemmas:Understanding human cooperation[M].Oxford:Oxford University Press,2014.
[3]叶航.公共合作中的社会困境与社会正义--基于计算机仿真的经济学跨学科研究[J].经济研究,2012(8):132-145.YE Hang.Social dilemma and social Justice in public cooperation[J].Economic Research Journal,2012(8):132-145.
[4]NOWAK M A,COAKLEY S.Evolution,games,and God[M].Cambridge:Harvard University Press,2013.
[5]ZHENG X D,LI C,YU J R,et al.A simple rule of direct reciprocity leads to the stable coexistence of cooperation and defection in the Prisoner's dilemma game[J].Journal of Theoretical Biology,2017,420:12-17.
[6]ZHANG C,ZHU Y,CHEN Z,et al.Punishment in the form of shared cost promotes altruism in the cooperative dilemma games[J].Journal of Theoretical Biology,2017,420:128-134.
[7]HAUSER O P,NOWAK M A,RAND D G.Punishment does not promote cooperation under exploration dynamics when anti-social punishment is possible[J].Journal of Theoretical Biology,2014,360:163-171.
[8]ALLEN B,LIPPNER G,CHEN Y,et al.Evolutionary dynamics on any population structure[J].Nature,2017,544(7649):227-230.
[9]REN J,WANG W X,QI F.Randomness enhances cooperation:a resonance-type phenomenon in evolutionary games[J].Physical Review E,2007,75(4):045101.
[10]RONG Z H,WU Z X.Effect of the degree correlation in public goods game on scale-free networks[J].EPL,2009,87:300013.
[11]FAN R,ZHANG Y,LUO M,et al.Promotion of cooperation induced by heterogeneity of both investment and payoff allocation in spatial public goods game[J].Physica A:Statistical Mechanics and its Applications,2017,465:454-463.
[12]汪小帆,刘亚冰.复杂网络中的社团结构算法综述[J].电子科技大学学报,2009,38(5):537-543.WANG Xiao-fan,LIU Ya-bing.Overview of algorithms for detecting community structure in complex networks[J].Journal of University of Electronic Science and Technology of China,2009,38(5):537-543.
[13]XIE F J,CUI W T,LIN J.Structural heterogeneity mediates the effect of community structure on cooperation[J].Complexity,2011,17(04):40-48.
[14]范如国,崔迎迎,张应青.多元偏好、社团结构与网络合作涌现仿真研究[J].复杂系统与复杂性科学,2016(4):26-34.FAN Ru-guo,Cui Ying-ying,ZHANG Ying-qing.Simulaition study of multi-preferences and community structure on the emergence of cooperation[J].Complex System and Complexity Science,2016(4):26-34.
[15]荣智海,吴枝喜,王文旭.共演博弈下网络合作动力学研究进展[J].电子科技大学学报,2013,42(1):10-22.RONG Zhi-hai,WU Zhi-xi,WANG Wen-xu.Research on the networked cooperative dynamics of Coevolutionary games[J].Journal of University of Electronic Science and Technology of China,2013,42(1):10-22.
[16]王龙,吴特,张艳玲.共演化博弈中的反馈机制[J].控制理论与应用,2014(7):823-836.WANG Long,WU Te,ZHANG Yan-ling.Feedback mechanism in coevolutionary games[J].Control Theory&Applications,2014(7):823-836.
[17]LI C,MAINI P K.An evolving network model with community structure[J].Journal of Physics A:Mathematical and General,2005,38(45):9741.
[18]KOMORITA S S,PARKS C D.Interpersonal relations:Mixed-motive interaction[J].Annual Review of Psychology,1995,46(1):183-207.
[19]SZABO G,TOKE C.Evolutionary prisoner’s dilemma game on a square lattice[J].Physical Review E,1998,58(1):69-73.
[20]HAUERT C,DOEBELI M.Spatial strueture often inhibits the evolution of cooperation in the snow-drift game[J].Nature,2004,428:643,646.
[21]SANTOS F C,PINHEIRO F L,LENAERTS T,et al.The role of diversity in the evolution of cooperation[J].Journal of Theoretical Biology,2012,299:88-96.
[22]GOMEZ-GARDENES J,CAMPILLO M,FLORIA L M,et al.Dynamical organization of cooperation in complex topologies[J].Physical Review Letters,2007,98(10):108103.
[23]DU W B,CAO X B,HU M B,et al.Effects of expectation and noise on evolutionary games[J].Physica A:Statistical Mechanics and Its Applications,2009,388(11):2215-2220.
[24]XIA C Y,MA Z Q,WANG Z,et al.Evaluating fitness by integrating the highest payoff within the neighborhood promotes cooperation in social dilemmas[J].Physica A:Statistical Mechanics and Its Applications,2012,391(24):6440-6447.