Review on Evolution of Cooperation in Social Dilemma Games
QUAN Ji1, ZHOU Yawen1, WANG Xianjia2
1.School of Management, Wuhan University of Technology, Wuhan 430070, China; 2.School of Economics and Management, Wuhan University, Wuhan 430072, China
Abstract：The conditions for the spontaneous emergence of cooperation under the complex human behavior model have become the focus of many disciplines. Exploring the conditions for cooperation has both important scientific significance and theoretical value for understanding the institutional arrangements in human society. The social dilemma games provide a theoretical prototype for studying cooperation issues between multiple individuals. As a dynamic analysis method that can describe individuals′ learning and strategy adjustment processes, evolutionary game theory has been one of the most effective frameworks for studying the evolution of cooperation. This review article systematically summarizes the research progress of using the evolutionary game method to study the issues of group cooperation in social dilemma games. Specifically, the following topics are included: research progress of (1) social dilemma game models, evolutionary game theory and equilibrium analysis methods, (2) social dilemma games and the evolution of cooperation under reward/punishment mechanism and reputation mechanism, (3) social dilemma games and the evolution of cooperation with separation strategy and extortion strategy, and (4) social dilemma games and the evolution of cooperation under the network reciprocity. Finally, prospects for further research issues in this area are presented.
全吉, 周亚文, 王先甲. 社会困境博弈中群体合作行为演化研究综述[J]. 复杂系统与复杂性科学, 2020, 17(1): 1-14.
QUAN Ji, ZHOU Yawen, WANG Xianjia. Review on Evolution of Cooperation in Social Dilemma Games. Complex Systems and Complexity Science, 2020, 17(1): 1-14.
[1]Kennedy D, Norman C. What don′t we know?[J]. Science,2005, 309(5731): 75-75. [2]Pennisi E. How did cooperative behavior evolve[J]. Science,2005, 309(5731): 93-93. [3]Nowak M A. Five rules for the evolution of cooperation[J]. Science,2006, 314(5805): 1560-1563. [4]黄少安, 张苏. 人类的合作及其演进研究[J]. 中国社会科学,2013, (07): 77-89. Huang Shaohan, Zhang Su. Research on human cooperation and its evolution[J]. Social Sciences in China, 2013, (07): 77-89. [5]张衔, 魏中许. 如何破解人类合作之谜——与黄少安教授商榷[J]. 中国社会科学,2016, (8): 90-94. Zhang Xian, Wei Zhongxu. How to solve the puzzle of human cooperation [J]. Social Sciences in China, 2016, (08): 90-94. [6]Tucker A W. A two-person dilemma[J]. Readings in games and information,1950: 7-8. [7]Rapoport A, Chammah A M. The game of chicken[J]. American Behavioral Scientist,1966, 10(3): 10-28. [8]Maynard Smith J, Price G R. The logic of animal conflict[J]. Nature,1973, 246(5427): 15-18. [9]Hamlin A, Sugden R. The Economics of Rights, Co-operation and Welfare[M]. Oxford: Blackwell Publisher, 1986. [10] Hardin G. The tragedy of the commons[J]. Science,1968, 162: 1243-1248. [11] Hamburger H. N-person prisoner′s dilemma[J]. Journal of Mathematical Sociology,1973, 3(1): 27-48. [12] Lugovskyy V, Puzzello D, Sorensen A, Walker J, Williams A. An experimental study of finitely and infinitely repeated linear public goods games[J]. Games and Economic Behavior,2017, 102: 286-302. [13] 刘小兵. 个人合作提供公共品的实验研究[J]. 管理世界,2004, (2): 50-55,96. Liu Xiaobing. Experimental study on public goods provided by individuals [J]. Management World, 2004, (02): 50-55,96. [14] 宋紫峰, 周业安, 何其新. 不平等厌恶和公共品自愿供给——基于实验经济学的初步研究[J]. 管理世界,2011, (12): 32-39,54,187. Song Zifeng, Zhou Yean, He Qixin. Inequality aversion and voluntary supply of public goods: a preliminary study based on experimental economics [J]. Management World, 2011, (12): 32-39,54,187. [15] Conlisk J. Why bounded rationality?[J]. Journal of economic literature,1996, 34(2): 669-700. [16] Maynard Smith J, Price G R. The logic of animal conflict[J]. Nature,1973, 246: 15-18. [17] Taylor P D, Jonker L B. Evolutionary stable strategies and game dynamics[J]. Mathematical biosciences,1978, 40(1-2): 145-156. [18] 王先甲, 全吉, 刘伟兵. 有限理性下的演化博弈与合作机制研究[J]. 系统工程理论与实践,2011, 31(Sup.1): 82-93. Wang Xianjia, Quan Ji, Liu Weibing. Research on Evolutionary Games and Cooperative Mechanisms under Bounded Rationality [J]. Systems Engineering: Theory & Practice, 2011, 31 (Sup.1): 82-93. [19] Foster D, Young P. Stochastic evolutionary game dynamics [J]. Theoretical population biology,1990, 38(2): 219-232. [20] Young P. The evolution of conventions[J]. Econometrica,1993, 61(1): 57-84. [21] Nowak M A, Sasaki A, Taylor C, et al. Emergence of cooperation and evolutionary stability in finite populations[J]. Nature,2004, 428(6983): 646-650. [22] Quan J, Wang X J. Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation[J]. Chinese Physics B,2011, 20(3): 030203. [23] Imhof L A, Nowak M A. Evolutionary game dynamics in a Wright-Fisher process[J]. Journal of mathematical biology,2006, 52(5): 667-681. [24] Quan J, Wang X J. Evolutionary game dynamics in a fitness-dependent wright-fisher process with noise[J]. Communications in Theoretical Physics,2011, 56(3): 404-410. [25] Huang W, Hauert C, Traulsen A. Stochastic game dynamics under demographic fluctuations[J]. Proceedings of the National Academy of Sciences of the United States of America,2015, 112(29): 9064-9069. [26] Liang H, Cao M, Wang X. Analysis and shifting of stochastically stable equilibria for evolutionary snowdrift games[J]. Systems & control letters,2015, 85: 16-22. [27] Quan J, Wang X J. Some analytic properties of the model for stochastic evolutionary games in finite populations with non-uniform interaction rate[J]. Communications in Theoretical Physics,2013, 60(1): 37-47. [28] Quan J, Liu W, Chu Y, Wang X. Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process[J]. Scientific Reports,2017, 7: 16110. [29] Wang X J, Quan J, Liu W B. Evolution of cooperation in continuous prisoner′s dilemma games on barabasi-albert networks with degree-dependent guilt mechanism[J]. Communications in Theoretical Physics,2012, 57(4): 897-903. [30] Fehr E, Gachter S. Cooperation and punishment in public goods experiments[J]. American Economic Review,2000, 90(90): 980-994. [31] Fowler J H. Altruistic punishment and the origin of cooperation[J]. Proceedings of the National Academy of Sciences of the United States of America,2005, 102(19): 7047-7049. [32] Colman A M. The puzzle of cooperation[J]. Nature,2006, 440(7085): 744-745. [33] Ozono H, Jin N, Watabe M, Shimizu K. Solving the second-order free rider problem in a public goods game: An experiment using a leader support system[J]. Scientific reports,2016, 6: 38349. [34] Ye H, Chen S, Luo J, Tan F, Jia Y M, Chen Y F. Increasing returns to scale: The solution to the second-order social dilemma[J]. Scientific reports,2016, 6: 31927. [35] Helbing D, Szolnoki A, Perc M, Szabó G. Punish, but not too hard: how costly punishment spreads in the spatial public goods game[J]. New Journal of Physics,2010, 12: 083005. [36] Helbing D, Szolnoki A, Perc M, Szabó G. Defector-accelerated cooperativeness and punishment in public goods games with mutations[J]. Physical Review E,2010, 81(5): 057104. [37] Quan J, Chu Y, Liu W, Wang X, Yang X. Stochastic evolutionary public goods game with first and second order costly punishments in finite populations[J]. Chinese Physics B,2018, 27(6): 060203. [38] Helbing D, Szolnoki A, Perc M, Szabó G. Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions[J]. PLoS Computational Biology,2010, 6(4): e1000758. [39] Rand D G, Nowak M A. The evolution of antisocial punishment in optional public goods games[J]. Nature communications,2011, 2: 434. [40] Gao J, Li Z, Cong R, Wang L. Tolerance-based punishment in continuous public goods game[J]. Physica a-Statistical Mechanics and Its Applications,2012, 391(16): 4111-4120. [41] Perc M, Szolnoki A. Self-organization of punishment in structured populations[J]. New Journal of Physics,2012, 14(4): 43013-43025. [42] Szolnoki A, Perc M. Effectiveness of conditional punishment for the evolution of public cooperation[J]. Journal of Theoretical Biology,2013, 325(10): 34-41. [43] Chen X, Szolnoki A, Perc M. Probabilistic sharing solves the problem of costly punishment[J]. New Journal of Physics,2014, 16(8): 083016. [44] Chen X, Sasaki T, Perc M. Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement[J]. Scientific reports,2015, 5: 17050. [45] Perc M, Szolnoki A. A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection games[J]. Scientific reports,2015, 5: 11027. [46] Liu L, Chen X, Szolnoki A. Competitions between prosocial exclusions and punishments in finite populations[J]. Scientific reports,2017, 7: 46634. [47] Perc M, Jordan J J, Rand D G, Wang Z, Boccaletti S, Szolnoki A. Statistical physics of human cooperation[J]. Physics reports,2017, 687: 1-51. [48] 连洪泉, 周业安, 左聪颖, 陈叶烽, 宋紫峰. 惩罚机制真能解决搭便车难题吗?——基于动态公共品实验的证据[J]. 管理世界,2013, (04): 69-81. Lian Hongquan, Zhou Yean, Zuo Congying, Chen Yefeng, Song Zifeng. Can the punishment mechanism really solve the free ride problem? ——Evidence based on dynamic public goods experiments [J]. Management World, 2013, (04): 69-81. [49] Nikiforakis N. Feedback, punishment and cooperation in public good experiments[J]. Games and Economic Behavior,2010, 68(2): 689-702. [50] 王龙, 丛睿, 李昆. 合作演化中的反馈机制[J]. 中国科学:信息科学,2014, (12): 1495-1514. Wang Long, Cong Rui, Li Kun. Feedback mechanism in cooperation evolving [J].Scientia Sinica Informationis, 2014, (12): 1495-1514. [51] 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——Interdisciplinary study of economics based on computer simulation [J]. Economic Research Journal, 2012, (08): 132-145. [52] 黄璜. 合作的逻辑:基于强欺骗策略的演化分析[J]. 管理科学学报,2013, (9): 1-8. Huang Y. The logic of cooperation: An evolutionary analysis based on strong deception strategy [J]. Journal of Management Sciences in China, 2013, (09): 1-8. [53] Kandori M. Social Norms and Community Enforcement[J]. The Review of Economic Studies,1992, 59(1): 63-80. [54] Nowak M A, Sigmund K. Evolution of indirect reciprocity by image scoring[J]. Nature,1998, 393(6685): 573-577. [55] Wedekind C, Milinski M. Cooperation through image scoring in humans[J]. Science,2000, 288(5467): 850-852. [56] Milinski M, Semmann D, Krambeck H. Reputation helps solve the ′tragedy of the commons′[J]. Nature,2002, 415(6870): 424-426. [57] Panchanathan K, Boyd R. Indirect reciprocity can stabilize cooperation without the second-order free rider problem[J]. Nature,2004, 432(7016): 499-502. [58] Nowak M A, Sigmund K. Evolution of indirect reciprocity[J]. Nature,2005, 437(7063): 1291-1298. [59] Ohtsuki H, Iwasa Y, Nowak M A. Indirect reciprocity provides a narrow margin of efficiency for costly punishment[J]. Nature,2009, 457(7225): 79-82. [60] Swakman V, Molleman L, Ule A, Egas M. Reputation-based cooperation: empirical evidence for behavioral strategies[J]. Evolution and Human Behavior,2016, 37(3): 230-235. [61] Ule A, Schram A, Riedl A, Cason T N. Indirect punishment and generosity toward Strangers[J]. Science,2009, 326(5960): 1701-1704. [62] Martinez-Vaquero L A, Cuesta J A. Evolutionary stability and resistance to cheating in an indirect reciprocity model based on reputation[J]. Physical Review E,2013, 87(5): 052810. [63] Uchida S, Sasaki T. Effect of assessment error and private information on stern-judging in indirect reciprocity[J]. Chaos Solitons & Fractals,2013, 56(7): 175-180. [64] Tanimoto J. Does information of how good or bad your neighbors are enhance cooperation in spatial Prisoner′s games?[J]. Chaos Solitons & Fractals,2017, 103: 184-193. [65] Berger U, Grune A. On the stability of cooperation under indirect reciprocity with first-order information[J]. Games and Economic Behavior,2016, 98: 19-33. [66] Santos F P, Pacheco J M, Santos F C. Evolution of cooperation under indirect reciprocity and arbitrary exploration rates[J]. Scientific reports,2016, 6: 37517. [67] Abbink K, Gangadharan L, Handfield T, Thrasher J. Peer punishment promotes enforcement of bad social norms[J]. Nature communications,2017, 8: 609. [68] Sasaki T, Okada I, Nakai Y. The evolution of conditional moral assessment in indirect reciprocity[J]. Scientific reports,2017, 7: 41870. [69] 张艳玲, 刘爱志, 孙长银. 间接互惠与合作演化的若干问题研究进展[J]. 自动化学报,2018, 44: 1-12. Zhang Yanling, Liu Aizhi, Sun Changyin. Development of several studies about indirect reciprocity and the evolution of cooperation[J]. Acta Automatica Sinica, 2018, 44: 1-12. [70] Hauert C, De Monte S, Hofbauer J, Sigmund K. Volunteering as red queen mechanism for cooperation in public goods games[J]. Science,2002, 296(5570): 1129-1132. [71] Brandt H, Hauert C, Sigmund K. Punishing and abstaining for public goods[J]. Proceedings of the National Academy of Sciences of the United States of America,2006, 103(2): 495-497. [72] Hauert C, Traulsen A, Brandt H, et al. Via freedom to coercion: The emergence of costly punishment[J]. Science,2007, 316(5833): 1905-1907. [73] Wang Z, Xu Z J, Zhang L Z. Punishment in optional public goods games[J]. Chinese Physics B,2010, 19(11): 0110201. [74] Xu Z, Wang Z, Zhang L. Bounded rationality in volunteering public goods games[J]. Journal of Theoretical Biology,2010, 264(1): 19-23. [75] Xu Z, Wang Z, Song H, Zhang L. Self-adjusting rule in spatial voluntary public goods games[J]. Epl,2010, 90(2): 20001. [76] Wu Z W, Xu Z J, Zhang L Z. Punishment mechanism with self-adjusting rules in spatial voluntary public goods games[J]. Communications in Theoretical Physics,2014, 62(5): 649-654. [77] Song Q Q, Li Z P, Fu C H, Wang L S. Optional contributions have positive effects for volunteering public goods games[J]. Physica a-Statistical Mechanics and Its Applications,2011, 390(23-24): 4236-4243. [78] Dercole F, De Carli M, Della Rossa F, Papadopoulos A V. Overpunishing is not necessary to fix cooperation in voluntary public goods games[J]. Journal of Theoretical Biology,2013, 326: 70-81. [79] Zhong L X, Xu W J, Shi Y D, Qiu T. Coupled dynamics of mobility and pattern formation in optional public goods games[J]. Chaos Solitons & Fractals,2013, 47: 18-26. [80] Nakamaru M, Yokoyama A. The effect of ostracism and optional participation on the evolution of cooperation in the voluntary public goods game[J]. Plos One,2014, 9(9): e108423. [81] Valverde P A, da Silva R, Stock E V. Global oscillations in the optional public goods game under spatial diffusion[J]. Physica a-Statistical Mechanics and Its Applications,2017, 474: 61-69. [82] Quan J, Liu W, Chu Y, Wang X. Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations[J]. Physica a-Statistical Mechanics and Its Applications,2018, 502: 123-134. [83] Press W H, Dyson F J. Iterated prisoner′s dilemma contains strategies that dominate any evolutionary opponent[J]. Proceedings of the National Academy of Sciences of the United States of America,2012, 109(26): 10409-10413. [84] Adami C, Hintze A. Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything[J]. Nature communications,2013, 4(4): 2193. [85] Hilbe C, Nowak M A, Sigmund K. Evolution of extortion in iterated prisoner’s dilemma games[J]. Proceedings of the National Academy of Sciences of the United States of America,2013, 110(17): 6913-6918. [86] Hilbe C, Nowak M A, Traulsen A. Adaptive dynamics of extortion and compliance[J]. Plos One,2013, 8(11): e77886. [87] Hilbe C, Martinez-Vaquero L A, Chatterjee K, et al. Memory-n strategies of direct reciprocity[J]. Proceedings of the National Academy of Sciences of the United States of America,2017, 114(18): 4715-4720. [88] Stewart A J, Plotkin J B. From extortion to generosity, evolution in the iterated prisoner′s dilemma[J]. Proceedings of the National Academy of Sciences of the United States of America,2013, 110(38): 15348-15353. [89] Hilbe C, Wu B, Traulsen A, Nowak M A. Cooperation and control in multiplayer social dilemmas[J]. Proceedings of the National Academy of Sciences of the United States of America,2014, 111(46): 16425-16430. [90] Szolnoki A, Perc M. Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations[J]. Scientific Reports,2014, 4: 5496. [91] Szolnoki A, Perc M. Evolution of extortion in structured populations[J]. Physical Review E,2014, 89(2): 022804. [92] Wu Z X, Rong Z. Boosting cooperation by involving extortion in spatial prisoner′s dilemma games[J]. Physical Review E,2014, 90(6): 062102. [93] Hao D, Rong Z H, Zhou T. Extortion under uncertainty: Zero-determinant strategies in noisy games[J]. Physical Review E,2015, 91(5): 052803. [94] Hilbe C, Traulsen A, Sigmund K. Partners or rivals? Strategies for the iterated prisoner′s dilemma[J]. Games and Economic Behavior,2015, 92: 41-52. [95] Lee C, Harper M, Fryer D. The art of war: beyond memory-one strategies in population games[J]. Plos One,2015, 10(3): 0120625. [96] Pan L, Hao D, Rong Z, et al. Zero-determinant strategies in iterated public goods game[J]. Scientific reports,2015, 5: 13096. [97] McAvoy A, Hauert C. Autocratic strategies for iterated games with arbitrary action spaces[J]. Proceedings of the National Academy of Sciences of the United States of America,2016, 113(13): 3573-3578. [98] Wang Z, Zhou Y, Lien J W, et al. Extortion can outperform generosity in the iterated prisoner′s dilemma[J]. Nature communications,2016, 7: 11125. [99] Xu B, Lan Y. The distribution of wealth and the effect of extortion in structured populations[J]. Chaos Solitons & Fractals,2016, 87: 276-280. [100] Xu B, Yue Y. The emergence of cooperation in tie strength models[J]. Chaos Solitons & Fractals,2016, 91: 585-590. [101] Xu X, Rong Z, Wu Z X, et al. Extortion provides alternative routes to the evolution of cooperation in structured populations[J]. Physical Review E,2017, 95(5): 052302. [102] Nowak M A, Robert M M. Evolutionary games and spatial chaos[J]. Nature,1992, 359(6398): 826-829. [103] Hauert C, Doebeli M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game[J]. Nature,2004, 428(6983): 643-646. [104] Vukov J, Szabo G. Evolutionary prisoner′s dilemma game on hierarchical lattices[J]. Physical Review E,2005, 71(3): 036133. [105] Perc M, Szolnoki A, Szabo G. Restricted connections among distinguished players support cooperation[J]. Physical Review E,2008, 78(6): 066101. [106] Szabó G, Szolnoki A. Cooperation in spatial prisoner′s dilemma with two types of players for increasing number of neighbors[J]. Physical Review E,2009, 79(1): 016106. [107] Jun T, Sethi R. Neighborhood structure and the evolution of cooperation[J]. Journal of Evolutionary Economics,2007, 17(5): 623-646. [108] Abramson G, Kuperman M. Social games in a social network[J]. Physical Review E,2001, 63(3): 030901. [109] Masuda N, Aihara K. Spatial prisoner′s dilemma optimally played in small-world networks[J]. Physics Letters A,2003, 313(1): 55-61. [110] Santos F C, Rodrigues J F, Pacheco J M. Epidemic spreading and cooperation dynamics on homogeneous small-world networks[J]. Physical Review E,2005, 72(5): 056128. [111] Wu Z X, Xu X J, Chen Y, Wang Y H. Spatial prisoner′s dilemma game with volunteering in Newman-Watts small-world networks[J]. Physical Review E,2005, 71(3): 037103. [112] Tomassini M, Luthi L, Giacobini M. Hawks and doves on small-world networks[J]. Physical Review E,2006, 73(1): 016132. [113] Zhong L X, Zheng D F, Zheng B, et al. Networking effects on cooperation in evolutionary snowdrift game[J]. Europhysics letters,2006, 76(4): 724-730. [114] 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. [115] 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. [116] Chen Y S, Lin H, Wu C X. Evolution of prisoner′s dilemma strategies on scale-free networks[J]. Physica a-Statistical Mechanics and Its Applications,2007, 385(1): 379-384. [117] Fu F, Chen X J, Liu L H, et al. Social dilemmas in an online social network: The structure and evolution of cooperation[J]. Physics Letters A,2007, 371(1): 58-64. [118] Assenza S, Gomez-Gardenes J, Latora V. Enhancement of cooperation in highly clustered scale-free networks[J]. Physical Review E,2008, 78(1): 017101. [119] Lee K H, Chan C H, Hui P M, et al. Cooperation in N-person evolutionary snowdrift game in scale-free Barabasi-Albert networks[J]. Physica a-Statistical Mechanics and Its Applications,2008, 387(22): 5602-5608. [120] 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. [121] Allen B, Lippner G, Chen Y, et al. Evolutionary dynamics on any population structure[J]. Nature,2017, 544(7649): 227-230. [122] Zimmermann M G, Eguiluz V M, San Miguel M. Coevolution of dynamical states and interactions in dynamic networks[J]. Physical Review E,2004, 69(6): 065102. [123] Zimmermann M G, Eguiluz V M. Cooperation, social networks, and the emergence of leadership in a prisoner′s dilemma with adaptive local interactions[J]. Physical Review E,2005, 72(5): 056118. [124] Pacheco J M, Traulsen A, Nowak M A. Coevolution of strategy and structure in complex networks with dynamical linking[J]. Physical Review Letters,2006, 97(25): 258103. [125] Pacheco J M, Traulsen A, Nowak M A. Active linking in evolutionary games[J]. Journal of Theoretical Biology,2006, 243(3): 437-443. [126] Santos F C, Pacheco J M, Lenaerts T. Cooperation prevails when individuals adjust their social ties[J]. PLoS Computational Biology,2006, 2(10): 1284-1291. [127] Szabó G, Szolnoki A, Varga M, Hanusovszky L. Ordering in spatial evolutionary games for pairwise collective strategy updates[J]. Physical Review E,2010, 82(2): 026110. [128] Liu Y K, Li Z, Chen X J, Wang L. Memory-based prisoner′s dilemma on square lattices[J]. Physica a-Statistical Mechanics and Its Applications,2010, 389(12): 2390-2396. [129] Cao X B, Zhang J, Fang Y P, Du W B. Promotion of cooperation in aspiration-based spatial prisoner′s dilemma game[J]. Physica a-Statistical Mechanics and Its Applications,2011, 390(12): 2258-2266. [130] Bo X Y. Other-regarding preference and the evolutionary prisoner′s dilemma on complex networks[J]. Physica a-Statistical Mechanics and Its Applications,2010, 389(5): 1105-1114. [131] Bo X Y, Ping C. Does social welfare preference always promote cooperation on barabasi and Albert Networks?[J]. Computational Economics,2011, 37(3): 249-266. [132] Chen X J, Fu F, Wang L. Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism[J]. Physica a-Statistical Mechanics and Its Applications,2008, 387(22): 5609-5615. [133] Chen X J, Wang L. Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game[J]. Physical Review E,2008, 77(1): 017103. [134] Pena J, Volken H, Pestelacci E, Tomassini M. Conformity hinders the evolution of cooperation on scale-free networks[J]. Physical Review E,2009, 80(1): 016110. [135] Quan J, Yang S, Wang X J. Learning algorithm and the cooperation behavior of continuous prisoner’s dilemma game on complex networks[J]. Journal of Information and Computational Science,2013, 10(10): 3031-3041. [136] Wang X, Lv S, Quan J. The evolution of cooperation in the prisoner’s dilemma and the snowdrift game based on particle swarm optimization[J]. Physica a-Statistical Mechanics and Its Applications,2017, 482: 286-295. [137] Vukov J, Szabo G, Szolnoki 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. [138] Szolnoki A, Perc M, Szabo G. Topology-independent impact of noise on cooperation in spatial public goods games[J]. Physical Review E,2009, 80(5): 056109. [139] Quan J, Wang X J. Effects of interaction rate and noise intensity on the equilibrium selection of a class of stochastic evolutionary games[J]. AISS: Advances in Information Sciences and Service Sciences,2013, 5(9): 224 - 233. [140] Perc M. Chaos promotes cooperation in the spatial prisoner′s dilemma game[J]. Europhysics letters,2006, 75(6): 841-846. [141] Chen X, Fu F, Wang L. Interaction stochasticity supports cooperation in spatial prisoner′s dilemma[J]. Physical Review E,2008, 78(5): 051120. [142] Cong R, Zhao Q C, Li K, Wang L. Individual mobility promotes punishment in evolutionary public goods games[J]. Scientific reports,2017, 7: 14015. [143] Li X, Jusup M, Wang Z, Li H, Shi L, Podobnik B, Stanley H, Havlin S, Boccaletti S. Punishment diminishes the benefits of network reciprocity in social dilemma experiments[J]. Proceedings of the National Academy of Sciences of the United States of America,2018, 115(1): 30-35.
