The evolution of cooperation in prisoner's dilemma game (PDG) and snow game (SG) on scale-free networks has been explored in this study. One-shot two-person game is played between neighbors on scale-free networks. Players have two possible strategies, cooperate or defect, and the strategies evolve according to the update rule of limited population analogue of replicator dynamics. Different from previous studies in which a player can interact with all his neighbors in every round of the game, this work proposes a new interaction pattern of players. A player can interact with at most W neighbors in every round of the game, who are named as interacting-neighbors. The value of W reflects the limited time and energy of players, and thus describes the limited interaction level of players in a networked PDG and SG. Results indicate that a high-level of cooperation in PDG and SG can be achieved on scale-free networks as long as high-connectivity players interact with a small fraction of their neighbors, and the interaction levels of players have significant positive effects on cooperation. These results suggest that even if individuals in real world have limited time and energy to interact with each other, they could still preserve cooperation because their interactions are rooted in actual scale-free networks. Moreover, high-connectivity individuals such as leaders or directors in an organization, who generally prefer interacting with each other in real world, play an important role in the evolution of cooperation. Current work provides a new interaction mechanism in networked game and contributes to understanding the emergence of cooperation in real society.
[1] Nowak M A. Five rules for the evolution of cooperation[J]. Science 2006, 314(5805), 1560-1563.
[2] Nowak M A, May R M. Evolutionary games and spatial chaos[J]. Nature,1992,359(6398):826-829.
[3] Szabó G, Toke C. Evolutionary prisoner's dilemma game on a square lattice[J]. Physical Review E, 1998, 58(1):69-73.
[4] 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.
[5] Vukov J, Szabo G, Szalnoki A. Cooperation in the noisy case:Prisoner's dilemma game on two types of regular random graphs[J]. Physical Review E, 2006, 73(6):067103.
[6] Szolnoki A, Szabo G. Cooperation enhanced by inhomogeneous activity of teaching forevolutionary Prisoner's Dilemma games[J]. Europhysics Letters, 2007,77(3):30004.
[7] PercM, Szolnoki A, SzabóG. Restricted connections among distinguished players support cooperation[J]. Physical Review E, 2008, 78(6):066101.
[8] Hauert C, Doebeli M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game[J]. Nature, 2004, 428(6983):643-646.
[9] 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.
[10] Santos F C, Pacheco J M, Lenaerts T. Evolutionary dynamics of social dilemmas in structured heterogeneous populations[J]. Proceedings of the National Academy of Sciences of the United States of America, 2006, 103(9):3490-3494.
[11] TomassiniM, Luthi L, Pestelacci E.Social dilemmas and cooperation in complex networks[J]. International Journal of Modern Physics C, 2007, 18(7):1173-1185.
[12] Wu Zhixi, Guan Jianyue, Xu X Jinjian, et al.Evolutionary prisoner's dilemma game on Barabási-Albert scale-free networks[J]. Physica A:Statistical Mechanics and its Applications, 2007, 379(2):672-680.
[13] Wu Yonghui, Li Xing, Zhang Zhongzhi, 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.
[14] Gómez-Gardeñes J, Poncela J, Floría L M, et al. Natural selection of cooperation and degree hierarchy in heterogeneous populations[J]. Journal of Theoretical Biology, 2008, 253(2):296-301.
[15] Assenza S, Gómez-Gardeñes J, Latora V. Enhancement of cooperation in highly clustered scale-free networks[J]. Physical Review E, 2008, 78(1):017101.
[16] 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.
[17] 林海, 吴晨旭. 基于遗传算法的重复囚徒困境博弈策略在复杂网络中的演化[J]. 物理学报, 2007, 56(8):4313-4318.
[18] 陈亮. 无标度网络中的公共物品博弈[J]. 苏州大学学报(自然科学版), 2009, 25(4):43-47.
[19] Gracia-Lázaro C, Ferrer A, Ruiz G, et al. Heterogeneous networks do not promote cooperation when humans play a Prisoner's Dilemma[J]. Proceedings of the National Academy of Sciences, 2012, 109(32):12922-12926.
[20] Grujić J, Fosco C, Araujo L, et al. Social experiments in the mesoscale:Humans playing a spatial prisoner's dilemma[J]. PloS One, 2010, 5(11):e13749-e13749.
[21] Traulsen A, Semmann D, Sommerfeld R D, et al. Human strategy updating in evolutionary games[J]. Proceedings of the National Academy of Sciences, 2010, 107(7):2962-2966.
[22] Grujić J, Gracia-Lázaro C, Milinski M, et al. A comparative analysis of spatial Prisoner's Dilemma experiments:Conditional cooperation and payoff irrelevance[J]. Scientific Reports, 2014,(4).
[23] Rand D G, Nowak M A, Fowler J H, et al. Static network structure can stabilize human cooperation[J]. Proceedings of the National Academy of Sciences, 2014, 111(48):17093-17098.
[24] Gracia-Lázaro C, Cuesta J A, Sánchez A, et al. Human behavior in prisoner's dilemma experiments suppresses network reciprocity[J]. Scientific Reports, 2012(2).
[25] Luthi L, Tomassini M, Pestelacci E. Evolutionary games on networks and payoff invariance under replicator dynamics[J]. Biosystems, 2009, 96(3):213-222.
[26] Xu Bo, Liu Lu, You Weijia. Importance of tie strengths in the prisoner's dilemma game on social networks[J]. Physics Letters A, 2011, 375(24):2269-2273.
[27] Fu Feng,Wu Te,Wang Long.Partner switching stabilizes cooperation in coevolutionary prisoner's dilemma[J]. Physical Review E, 2009,79(2):036101-1-036101-7.
[28] Kim J W. A tag-based evolutionary prisoner's dilemma game on networks with different topologies[J]. Journal of Artificial Societies and Social Simulation, 2010, 13(3):1-17.
[29] Bausch A W.Stochastic interactions increase cooperation in a spatial Prisoner's Dilemma[J]. Complexity, 2014,21(2):82-92.
[30] Barabási A L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439):509-512.
[31] Doebeli M, Hauert C. Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game[J]. Ecology Letters, 2005, 8(7):748-766.
[32] 张宏娟, 范如国. 基于复杂网络演化博弈的传统产业集群低碳演化模型研究[J]. 中国管理科学, 2014, 22(12):41-47.
[33] 吴结兵, 郭斌. 企业适应性行为, 网络化与产业集群的共同演化——绍兴县纺织业集群发展的纵向案例研究[J]. 管理世界, 2010,(2):141-155.
