Abstract：In order to study the influence of higher-order structures on the evolution of cooperative behavior on scale-free networks, a network game model based on the Prisoner's Dilemma game is constructed. A second-order higher-order structure is introduced on the scale-free network, a triangular face game containing pairwise games is defined, and the higher-order structure parameters are used to link the pairwise game payoffs with the face game payoffs, and the influence of the higher-order structure on the evolution of cooperative behavior is analyzed through simulation experiments. The results show that when individuals with high connectivity prioritize cooperation and obtain high payoffs, other individuals with high connectivity will be prompted to choose cooperation, and once a stable "all-cooperative" triangular strategy structure is formed among individuals, the payoffs of each cooperator can be significantly increased, which in turn promotes the emergence of cooperative behaviors.
谢逢洁, 姚欣, 王思一. 高阶结构对无标度网络上合作行为演化的影响[J]. 复杂系统与复杂性科学, 2024, 21(1): 12-19.
XIE Fengjie, YAO Xin, WANG Siyi. The Effect of Higher-order Structure on the Evolution of Cooperative Behavior on Scale-free Networks[J]. Complex Systems and Complexity Science, 2024, 21(1): 12-19.
[1] NOWAK M A. Five rules for the evolution of cooperation[J]. Science,2006,314(5805):1560-1563. [2] WEIBULL J W. Evolutionary game theory[M]. Cambridge: MIT Press,1997. [3] NOWAK M A, MAY R M. Evolutionary games and spatial chaos[J]. Nature,1992,359(6398):826-829. [4] SZABÓ G, TÖKE C. Evolutionary prisoner's dilemma game on a square lattice[J]. Physical Review E,1998,58(1):69. [5] SZABÓ G, VUKOV J, SZOLNOKI A. Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices[J]. Physical Review E,2005,72(4):047107. [6] PERC M, SZOLNOKI A. Social diversity and promotion of cooperation in the spatial prisoner's dilemma game[J]. Physical Review E,2008,77(1):011904. [7] SANTOS F C, SANTOS M D, PACHECO J M. Social diversity promotes the emergence of cooperation in public goods games[J]. Nature,2008,454(7201):213-216. [8] LIMING W, WU F. Effects of empty sites on cooperation in the prisoner's dilemma game based on social diversity[J]. Discrete Dynamics in Nature and Society, 2014,2014(1):1-8. [9] XIA C Y, MENG X K, WANG Z. Heterogeneous coupling between interdependent lattices promotes the cooperation in the prisoner's dilemma game[J]. PloS One,2015,10(6): e0129542. [10] ZHU C, SUN S, WANG J, et al. Role of population density and increasing neighborhood in the evolution of cooperation on diluted lattices[J]. Physica A: Statistical Mechanics and Its Applications,2013,392(24):6353-6360. [11] BARABÁSI A L, ALBERT R. Emergence of scaling in random networks[J]. Science,1999,286(5439):509-512. [12] SANTOS F C, PACHECO J M. Scale-free networks provide a unifying framework for the emergence of cooperation[J]. Physical Review Letters,2005,95(9):098104. [13] 谢逢洁,崔文田,孙笑明.无标度网络的群聚性对合作行为的影响[J].系统工程学报,2010,25(2):152-158. XIE F J, CUI W T, SUN X M. Influence of clustering on cooperative behavior in scale-free networks[J]. Journal of Systems Engineering,2010,25(2):152-158. [14] WU Y, LI X, ZHANG Z, et al. The different cooperative behaviors on a kind of scale-free networks with identical degree sequence[J]. Chaos, Solitons & Fractals,2013,56:91-95.[15] 谢逢洁,武小平,崔文田,等.博弈参与水平对无标度网络上合作行为演化的影响[J].中国管理科学,2017,25(5):116-124. XIE F J, WU X P, CUI W T, et al. Influence of game participation level on the evolution of cooperative behavior in scale-free networks[J]. Chinese Journal of Management Science,2017,25(5):116-124. [16] MAO Y J, RONG Z H, WU Z X, et al. Effect of collective influence on the evolution of cooperation in evolutionary prisoner's dilemma games[J]. Applied Mathematics and Computation,2021,392:125679. [17] HU X T, WU M Y. The analysis of evolutionary prisoner's dilemma game based on weighting effect[J]. International Journal of Modern Physics C,2021,32(5):2150066. [18] ASSENZA S, GÓMEZ-GARDEÓES J, LATORA V. Enhancement of cooperation in highly clustered scale-free networks[J]. Physical Review E,2008,78(1):017101. [19] KLEINEBERG K K. Metric clusters in evolutionary games on scale-free networks[J]. Nature Communications, 2017,8(1):1-8. [20] XIE F J, CUI W T, LIN J. Structural heterogeneity mediates the effect of community structure on cooperation[J]. Complexity,2012,17(4):40-48. [21] ZHANG J L, ZHU Y Y, CHEN Z Q, et al. Evolutionary game dynamics of multiagent systems on multiple community networks[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems,2019,50(11):1-17. [22] RONG Z H, LI X, WANG X F. Roles of mixing patterns in cooperation on a scale-free networked game[J]. Physical Review E,2007,76(2):027101. [23] WANG Z, WANG L, PERC M, et al. Degree mixing in multilayer networks impedes the evolution of cooperation[J]. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics,2014,89(5):052813. [24] BATTISTON F, CENCETTI G, IACOPINI I, et al. Networks beyond pairwise interactions: structure and dynamics[J]. Physics Reports,2020,874:1-92. [25] MAJHI S, PERC M, GHOSH D. Dynamics on higher-order networks: a review[J]. Journal of the Royal Society Interface,2022,19(188):20220043. [26] IACOPINI I, PETRI G, BARRAT A, et al. Simplicial models of social contagion[J]. Nature Communi-cations,2019,10(1):1-9. [27] WANG D, ZHAO Y, LENG H, et al. A social communication model based on simplicial complexes[J]. Physics Letters A,2020,384(35):126895. [28] KUMAR A, CHOWDHARY S, CAPRARO V, et al. Evolution of honesty in higher-order social networks[J]. Physical Review E,2021,104(5):054308. [29] SKARDAL P S, AROLA-FERNáNDEZ L, TAYLOR D, et al. Higher-order interactions can better optimize network synchronization[J]. Physical Review Research,2021,3(4):043193. [30] BATTISTON F, AMICO E, BARRAT A, et al. The physics of higher-order interactions in complex systems[J]. Nature Physics,2021,17(10):1093-1098. [31] CENCETTI G, BATTISTON F, LEPRI B, et al. Temporal properties of higher-order interactions in social networks[J]. Scientific Reports,2021,11(1):7028. [32] MALETIC' S, ANDJELKOVIC' M, RAJKOVIC' M. Potential grouping of nodes induced by higher-order structures in complex networks[J]. Chaos,2021,31(12):123115. [33] SHI D H, CHEN G R. Simplicial networks: a powerful tool for characterizing higher-order interactions[J]. National Science Review,2022,9(5): nwac038.
