数据驱动的人类合作和竞争行为研究动态

doi:10.15960/j.cnki.issn.1007-6093.2025.02.001

摘要/Abstract

摘要：

如何促进人类社会中的合作和良性竞争, 一直是经济学和管理学中的核心问题。传统研究大多基于经典博弈论方法, 通过纳什均衡分析设计管理机制, 但是现实中人们的行为往往会背离均衡。近年来, 从实验和实证数据出发, 综合博弈论和行为经济学方法研究合作和竞争行为已经成为经济和管理学主流方向之一。本文将首先简要介绍数据驱动的人类行为和机制设计主要研究方法, 包括博弈论、行为经济学、心理学和神经科学等。接下来从影响合作和竞争行为的内在因素、外在因素和制度因素三个维度, 总结数据驱动的人类合作和竞争问题的研究动态。最后, 本文列出了一些当前研究中存在的挑战性问题。

关键词: 博弈论, 行为经济学, 合作, 竞争

Abstract:

The promotion of cooperation and fair competition is one of the key questions in economics and management science. Most of previous studies in this field applied game theory method. These studies often designed management mechanism based on the Nash equilibrium analysis. However, people in reality are boundedly rational and often deviate from the Nash equilibrium. In recent years, data driven analysis for human cooperation and competition behaviors becomes one of the mainstream directions of economics and management science. This paper provides a survey of this field. We first introduce some theoretical and data driven methods for analyzing human behavior and mechanism design, including Nash equilibrium analysis, evolutionary game theory, cooperative game theory, behavioral economics, experimental economics, psychology, and neuroscience methods. Then we discuss internal factors, external factors, and institutional factors that may affect human cooperation and competition. For internal factors, we focus on prosocial preferences, such as altruism, reciprocity, fairness, and trust. We summarize related empirical results and discuss the neural and evolutionary mechanisms of these prosocial preferences. For external factors, we focus on the influences of social norm, network structure, and information structure on cooperation and competition. For institutional factors, we discuss the effects of different types of reputation mechanisms and incentive mechanisms. Finally, some challenging questions in this field are discussed.

Key words: game theory, behavioral economics, cooperation, competition

中图分类号:

O225

董雅丽, 康恺, 张博宇. 数据驱动的人类合作和竞争行为研究动态[J]. 运筹学学报（中英文）, 2025, 29(2): 1-20.

Yali DONG, Kai KANG, Boyu ZHANG. A survey of data driven approach for human cooperation and competition[J]. Operations Research Transactions, 2025, 29(2): 1-20.

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参考文献 79

80	Lergetporer P , Angerer S , Glätzle-Rützler D , et al. Third-party punishment increases cooperation in children through (misaligned) expectations and conditional cooperation[J]. Proceedings of the National Academy of Sciences USA, 2014, 111 (19): 6916- 6921. doi: 10.1073/pnas.1320451111
81	Jackson M O . Social and Economic Networks[M]. Princeton: Princeton University Press, 2010.
82	Barabasi A L . Linked: How Everything is Connected to Everything Else and What It Means for Business, Science, and Everyday Life[M]. New York: Basic Books, 2014.
83	Watts D J , Strogatz S H . Collective dynamics of 'small-world' networks[J]. Nature, 1998, 393 (6684): 440- 442. doi: 10.1038/30918
84	Newman M , Barabási A , Watts D J . The Structure and Dynamics of Networks[M]. Princeton: Princeton University Press, 2006.
85	Rand D G , Arbesman S , Christakis N A . Dynamic social networks promote cooperation in experiments with humans[J]. Proceedings of the National Academy of Sciences USA, 2011, 108 (48): 19193- 19198. doi: 10.1073/pnas.1108243108
86	Melamed D , Harrell A , Simpson B . Cooperation, clustering, and assortative mixing in dynamic networks[J]. Proceedings of the National Academy of Sciences USA, 2018, 115 (5): 951- 956. doi: 10.1073/pnas.1715357115
87	Ohtsuki H , Hauert C , Lieberman E , et al. A simple rule for the evolution of cooperation on graphs and social networks[J]. Nature, 2006, 441 (7092): 502- 505. doi: 10.1038/nature04605
88	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. doi: 10.1038/nature06940
89	Zhang B , Li C , Tao Y . Evolutionary stability and the evolution of cooperation on heterogeneous graphs[J]. Dynamic Games and Applications, 2016, 6 (4): 567- 579. doi: 10.1007/s13235-015-0146-2
90	Allen B , Lippner G , Chen Y , et al. Evolutionary dynamics on any population structure[J]. Nature, 2017, 544 (7649): 227- 230. doi: 10.1038/nature21723
1	Kennedy D , Norman C . What don't we know[J]. Science, 2005, 309 (5731): 75. doi: 10.1126/science.309.5731.75
2	黄少安, 韦倩. 利他经济学研究评述[J]. 经济学动态, 2008, 4, 98- 102.
3	黄少安, 张苏. 人类的合作及其演进研究[J]. 中国社会科学, 2013, 7, 77- 89.
4	Axelord R . The Evolution of Cooperation[M]. New York: Basic Books, 1984.
5	Ostrom E . Understanding Institutional Diversity[M]. Princeton: Princeton University Press, 2005.
6	Dixit A , Skeath S , Reiley D . Games of Strategy[M]. New York: W. W. Norton & Company, 2015.
7	Sigmund K . The Calculus of Selfishness[M]. Princeton: Princeton University Press, 2010.
8	Fudenberg D , Tirole J . Game Theory[M]. Cambridge: MIT Press, 1995.
9	Nash J F . The bargaining problem[J]. Econometrica, 1950, 18 (2): 155- 162. doi: 10.2307/1907266
10	Rubinstein A . Perfect equilibrium in a bargaining model[J]. Econometrica, 1982, 50 (1): 97- 109. doi: 10.2307/1912531
11	Güth W , Schmittberger R , Schwarze B . An experimental analysis of ultimatum bargaining[J]. Journal of Economic Behavior and Organization, 1982, 3 (4): 367- 388. doi: 10.1016/0167-2681(82)90011-7
91	Cassar A . Coordination and cooperation in local, random and small world networks: Experimental evidence[J]. Games and Economic Behavior, 2007, 58 (2): 209- 230. doi: 10.1016/j.geb.2006.03.008
92	Traulsen A , Semmann D , Sommerfeld R D , et al. Human strategy updating in evolutionary games[J]. Proceedings of the National Academy of Sciences USA, 2010, 107 (7): 2962- 2966. doi: 10.1073/pnas.0912515107
93	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 USA, 2012, 109 (32): 12922- 12926. doi: 10.1073/pnas.1206681109
94	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 USA, 2014, 111 (48): 17093- 17098. doi: 10.1073/pnas.1400406111
95	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 (1): 1- 9.
96	Ohtsuki H , Iwasa Y . The leading eight: Social norms that can maintain cooperation by indirect reciprocity[J]. Journal of Theoretical Biology, 2006, 239 (4): 435- 444. doi: 10.1016/j.jtbi.2005.08.008
97	Nishi A , Shirado H , Rand D G , et al. Inequality and visibility of wealth in experimental social networks[J]. Nature, 2015, 526 (7573): 426- 429. doi: 10.1038/nature15392
98	Page K M , Nowak M A , Sigmund K . The spatial ultimatum game[J]. Proceedings of the Royal Society B: Biological Sciences, 2000, 267 (1458): 2177- 2182. doi: 10.1098/rspb.2000.1266
99	Szolnoki A , Perc M , Szabó G . Defense mechanisms of empathetic players in the spatial ultimatum game[J]. Physical Review Letters, 2012, 109 (7): 078701. doi: 10.1103/PhysRevLett.109.078701
100	Han X , Cao S , Bao J , et al. Equal status in Ultimatum Games promotes rational sharing[J]. Scientific Reports, 2018, 8 (1): 1222. doi: 10.1038/s41598-018-19503-x
101	Han X , Cao S , Shen Z , et al. Emergence of communities and diversity in social networks[J]. Proceedings of the National Academy of Sciences USA, 2017, 114 (11): 2887- 2891. doi: 10.1073/pnas.1608164114
12	何韵文, 郑捷. 拍卖机制与竞价行为: 基于付费竞价式拍卖的理论与实验[J]. 经济研究, 2021, 56 (11): 192- 208. doi: 10.12229/j.issn.1672-5719.2021.11.127
13	Brandenburger A , Stuart H . Biform games[J]. Management Science, 2007, 53 (4): 537- 549. doi: 10.1287/mnsc.1060.0591
14	Kalai A , Kalai E . Cooperation in strategic games revisited[J]. Quarterly Journal of Economics, 2013, 128 (2): 917- 966. doi: 10.1093/qje/qjs074
15	Nash J F . Equilibrium points in n-person games[J]. Proceedings of the National Academy of Sciences USA, 1950, 36 (1): 48- 49. doi: 10.1073/pnas.36.1.48
16	Maynard S J . Evolution and the Theory of Games[M]. Cambridge: Cambridge University Press, 1982.
17	Harsanyi J C , Selten R . A General Theory of Equilibrium Selection in Games[M]. Cambridge: MIT Press, 1988.
18	Kandori M , Mailath G J , Rob R . Learning, mutation, and long run equilibria in games[J]. Econometrica, 1993, 61 (1): 29- 56. doi: 10.2307/2951777
19	McKelvey R D , Palfrey T R . Quantal response equilibria in normal form games[J]. Games and Economic Behavior, 1995, 10 (1): 6- 38. doi: 10.1006/game.1995.1023
20	Sandholm W H . Population Games and Evolutionary Dynamics[M]. Cambridge: MIT Press, 2010.
21	Weibull J W . Evolutionary Game Theory[M]. Cambridge: MIT Press, 1995.
22	Nowak M A . Evolutionary Dynamics: Exploring the Equations of Life[M]. Cambridge: Harvard University Press, 2006.
102	Acemoǧlu D , Como G , Fagnani F , et al. Opinion fluctuations and disagreement in social networks[J]. Mathematics of Operations Research, 2013, 38 (1): 1- 27. doi: 10.1287/moor.1120.0570
103	Kearns M , Judd S , Tan J , et al. Behavioral experiments on biased voting in networks[J]. Proceedings of the National Academy of Sciences USA, 2009, 106 (5): 1347- 1352. doi: 10.1073/pnas.0808147106
104	Bond R M , Fariss C J , Jones J J , et al. A 61-million-person experiment in social influence and political mobilization[J]. Nature, 2012, 489 (7415): 295- 298. doi: 10.1038/nature11421
105	Stewart A J , Mosleh M , Diakonova M , et al. Information gerrymandering and undemocratic decisions[J]. Nature, 2019, 573 (7772): 117- 121. doi: 10.1038/s41586-019-1507-6
106	Del Vicario M , Bessi A , Zollo F , et al. The spreading of misinformation online[J]. Proceedings of the National Academy of Sciences USA, 2016, 113 (3): 554- 559. doi: 10.1073/pnas.1517441113
107	Vosoughi S , Roy D , Aral S . The spread of true and false news online[J]. Science, 2018, 359 (6380): 1146- 1151. doi: 10.1126/science.aap9559
108	Pennycook G , Rand D G . Fighting misinformation on social media using crowd-sourced judgments of news source quality[J]. Proceedings of the National Academy of Sciences USA, 2019, 116 (7): 2521- 2526. doi: 10.1073/pnas.1806781116
109	Bail C A , Argyle L P , Brown T W , et al. Exposure to opposing views on social media can increase political polarization[J]. Proceedings of the National Academy of Sciences USA, 2018, 115 (37): 9216- 9221. doi: 10.1073/pnas.1804840115
110	Horváth G , Kovářík J , Mengel F . Limited memory can be beneficial for the evolution of cooperation[J]. Journal of Theoretical Biology, 2012, 300 (1): 193- 205.
111	Ma S , Zhang B , Cao S , et al. Limited memory optimizes cooperation in social dilemma experiments[J]. Royal Society Open Science, 2021, 8 (8): 210653. doi: 10.1098/rsos.210653
112	Charness G , Dufwenberg M . Promises and partnership[J]. Econometrica, 2006, 74 (6): 1579- 1601. doi: 10.1111/j.1468-0262.2006.00719.x
23	Fudenberg D , Levine D K . The Theory of Learning in Games[M]. Cambridge: MIT Press, 1998.
24	Maynard S J , Price G R . The logic of animal conflict[J]. Nature, 1973, 246 (5427): 15- 18. doi: 10.1038/246015a0
25	Taylor P D , Jonker L B . Evolutionary stable strategies and game dynamics[J]. Mathematical Biosciences, 1978, 40 (1-2): 145- 156. doi: 10.1016/0025-5564(78)90077-9
26	Hofbauer J , Sigmund K . Evolutionary Games and Population Dynamics[M]. Cambridge: Cambridge University Press, 1998.
27	Zhang B , Pei S . Game theory and the evolution of cooperation[J]. Journal of the Operations Research Society of China, 2022, 10 (2): 379- 399. doi: 10.1007/s40305-021-00350-z
28	Peleg B, Sudhölter P. Introduction to the Theory of Cooperative Games [M]. Heidelberg: Springer, 2007.
29	Shapley L S . Contributions to the Theory of Games[M]. Princeton: Princeton University Press, 1953.
30	Camerer C . Behavioral Game Theory: Experiments in Strategic Interaction[M]. Princeton: Princeton University Press, 2003.
31	Fehr E , Fischbacher U . The nature of human altruism[J]. Nature, 2003, 425 (6960): 785- 791. doi: 10.1038/nature02043
32	汪丁丁. 行为经济学讲义: 演化论的视角[M]. 上海: 上海人民出版社, 2011.
33	姜树广, 韦倩. 信念与心理博弈: 理论、实证与应用[J]. 经济研究, 2013, 48 (6): 141- 154.
113	Tavoni A , Dannenberg A , Kallis G , et al. Inequality, communication, and the avoidance of disastrous climate change in a public goods game[J]. Proceedings of the National Academy of Sciences USA, 2011, 108 (29): 11825- 11829. doi: 10.1073/pnas.1102493108
114	Hauert C , De Monte S , Hofbauer J , et al. Volunteering as red queen mechanism for cooperation in public goods games[J]. Science, 2002, 296 (5570): 1129- 1132. doi: 10.1126/science.1070582
115	Milinski M , Semmann D , Krambeck H J . Volunteering leads to rock-paper-scissors dynamics in a public goods game[J]. Nature, 2003, 425 (6956): 390- 393. doi: 10.1038/nature01986
116	Fujiwara-Greve T , Okuno-Fujiwara M . Voluntarily separable repeated prisoner's dilemma[J]. The Review of Economic Studies, 2009, 76 (3): 993- 1021. doi: 10.1111/j.1467-937X.2009.00539.x
117	Fehl K , van der Post D J , Semmann D . Co-evolution of behaviour and social network structure promotes human cooperation[J]. Ecology Letters, 2011, 14 (6): 546- 551. doi: 10.1111/j.1461-0248.2011.01615.x
118	Zhang B , Fan S , Li C , et al. Opting out against defection leads to stable coexistence with cooperation[J]. Scientific Reports, 2016, 6 (1): 35902- 35902. doi: 10.1038/srep35902
119	Ye M , Zheng J , Nikolov P , et al. One step at a time: Does gradualism build coordination[J]. Management Science, 2020, 66 (1): 113- 129. doi: 10.1287/mnsc.2018.3210
120	Nowak M A , Sigmund K . Evolution of indirect reciprocity[J]. Nature, 2005, 437 (7063): 1291- 1298. doi: 10.1038/nature04131
121	Schmid L , Chatterjee K , Hilbe C , et al. A unified framework of direct and indirect reciprocity[J]. Nature Human Behaviour, 2021, 5 (10): 1292- 1302. doi: 10.1038/s41562-021-01114-8
122	Santos F P , Santos F C , Pacheco J M . Social norm complexity and past reputations in the evolution of cooperation[J]. Nature, 2018, 555 (7695): 242- 245. doi: 10.1038/nature25763
123	Nowak M A , Sigmund K . Evolution of indirect reciprocity by image scoring[J]. Nature, 1998, 393 (6685): 573- 577. doi: 10.1038/31225
34	叶航, 陈叶烽, 贾拥民. 超越经济人: 人类的亲社会行为与社会偏好[M]. 上海: 高等教育出版社, 2013.
35	Andreoni J , Miller J . Giving according to GARP: An experimental test of the consistency of preferences for altruism[J]. Econometrica, 2002, 70 (2): 737- 753. doi: 10.1111/1468-0262.00302
36	Charness G , Rabin M . Understanding social preferences with simple tests[J]. The Quarterly Journal of Economics, 2002, 117 (3): 817- 869. doi: 10.1162/003355302760193904
37	Peysakhovich A , Nowak M A , Rand D G . Humans display a 'cooperative phenotype' that is domain general and temporally stable[J]. Nature Communications, 2014, 5 (1): 4939. doi: 10.1038/ncomms5939
38	Fischbacher U , Gächter S , Fehr E . Are people conditionally cooperative? Evidence from a public goods experiment[J]. Economics Letters, 2001, 71 (3): 397- 404. doi: 10.1016/S0165-1765(01)00394-9
39	Kurzban R , Houser D . Experiments investigating cooperative types in humans: A complement to evolutionary theory and simulations[J]. Proceedings of the National Academy of Sciences USA, 2005, 102 (5): 1803- 1807. doi: 10.1073/pnas.0408759102
40	Dong Y , Li C , Tao Y , Zhang B . Evolution of conformity in social dilemmas[J]. Plos One, 2015, 10 (9): e0137435. doi: 10.1371/journal.pone.0137435
41	Yang C , Zhang B , Charness G , et al. Endogenous rewards promote cooperation[J]. Proceedings of the National Academy of Sciences USA, 2018, 115 (40): 9968- 9973. doi: 10.1073/pnas.1808241115
42	Fehr E , Schmidt K M . A theory of fairness, competition, and cooperation[J]. The Quarterly Journal of Economics, 1999, 114 (3): 817- 868. doi: 10.1162/003355399556151
43	Bolton G E , Ockenfels A . ERC: A theory of equity, reciprocity, and competition[J]. The American Economic Review, 2000, 90 (1): 166- 193. doi: 10.1257/aer.90.1.166
44	Bear A , Rand D G . Intuition, deliberation, and the evolution of cooperation[J]. Proceedings of the National Academy of Sciences USA, 2016, 113 (4): 936- 941. doi: 10.1073/pnas.1517780113
124	Wedekind C , Milinski M . Cooperation through image scoring in humans[J]. Science, 2000, 288 (5467): 850- 852. doi: 10.1126/science.288.5467.850
125	Milinski M , Semmann D , Bakker T C M , et al. Cooperation through indirect reciprocity: Image scoring or standing strategy[J]. Proceedings of the Royal Society B: Biological Sciences, 2001, 268 (1484): 2495- 2501. doi: 10.1098/rspb.2001.1809
126	Yoeli E , Hoffmanbc M , Rand D G , et al. Powering up with indirect reciprocity in a large-scale field experiment[J]. Proceedings of the National Academy of Sciences USA, 2013, 110 (2): 10424- 10429.
127	Khadjavi M . Indirect reciprocity and charitable giving-evidence from a field experiment[J]. Management Science, 2017, 63 (11): 3708- 3717. doi: 10.1287/mnsc.2016.2519
128	Clark D , Fudenberg D , Wolitzky A . Indirect reciprocity with simple records[J]. Proceedings of the National Academy of Sciences USA, 2020, 117 (21): 11344- 11349. doi: 10.1073/pnas.1921984117
129	Balliet D , Mulder L B , Van Lange P A M . Reward, punishment, and cooperation: A meta-analysis[J]. Psychological Bulletin, 2011, 137 (4): 594- 615. doi: 10.1037/a0023489
130	Guala F . Reciprocity: Weak or strong? What punishment experiments do (and do not) demonstrate[J]. Behavioral and Brain Sciences, 2012, 35 (1): 1- 15. doi: 10.1017/S0140525X11000069
131	Perc M , Jordan J J , Rand D G , et al. Statistical physics of human cooperation[J]. Physics Reports, 2017, 687, 1- 51. doi: 10.1016/j.physrep.2017.05.004
132	Sigmund K , Hauert C , Nowak M A . Reward and punishment[J]. Proceedings of the National Academy of Sciences USA, 2001, 98 (19): 10757- 10762. doi: 10.1073/pnas.161155698
133	Bowles S , Gintis H . A Cooperative Species: Human Reciprocity and Its Evolution[M]. Princeton: Princeton University Press, 2011.
134	Fehr E , Gächter S . Cooperation and punishment in public goods experiments[J]. The American Economic Review, 2000, 90 (4): 980- 994. doi: 10.1257/aer.90.4.980
45	Glimcher P W . Foundations of Neuroeconomic Analysis[M]. Oxford: Oxford University Press, 2010.
46	Henrich J , Boyd R , Bowles S , et al. In search of homo economicus: Behavioral experiments in 15 small-scale societies[J]. The American Economic Review, 2001, 91 (2): 73- 78. doi: 10.1257/aer.91.2.73
47	Kagel J H , Roth A E . The Handbook of Experimental Economics[M]. Princeton: Princeton University Press, 1995.
48	Fischbacher U , Gächter S . Social preferences, beliefs, and the dynamics of free riding in public goods experiments[J]. The American Economic Review, 2010, 100 (1): 541- 556. doi: 10.1257/aer.100.1.541
49	Oosterbeek H , Sloof R , van de Kuilen G . Cultural differences in ultimatum game experiments: Evidence from a meta-analysis[J]. Experimental Economics, 2004, 7 (2): 171- 188. doi: 10.1023/B:EXEC.0000026978.14316.74
50	Sanfey A G . Social decision-making: Insights from game theory and neuroscience[J]. Science, 2007, 318 (5850): 598- 602. doi: 10.1126/science.1142996
51	Declerck C H , Boone C . Neuroeconomics of Prosocial Behaviour: The Compassionate Egoist[M]. New York: Academic Press, 2016.
52	Blake P R , McAuliffe K , Corbit J , et al. The ontogeny of fairness in seven societies[J]. Nature, 2015, 528 (7581): 258- 261. doi: 10.1038/nature15703
53	Gao X , Yu H , Sáez I , et al. Distinguishing neural correlates of context dependent advantageous and disadvantageous inequity aversion[J]. Proceedings of the National Academy of Sciences USA, 2018, 115 (33): 7680- 7689.
54	Zak P J , Kurzban R , Matzner W T . The neurobiology of trust[J]. Annals of the New York Academy of Sciences, 2004, 1032 (1): 224- 227. doi: 10.1196/annals.1314.025
55	Kosfeld M , Heinrichs M , Zak P J , et al. Oxytocin increases trust in humans[J]. Nature, 2005, 435 (7042): 673- 676. doi: 10.1038/nature03701
135	Rand D G , Dreber A , Ellingsen T , et al. Positive interactions promote public cooperation[J]. Science, 2009, 325 (5945): 1272- 1275. doi: 10.1126/science.1177418
136	Sutter M , Haigner S , Kocher M G . Choosing the carrot or the stick? Endogenous institutional choice in social dilemma situations[J]. The Review of Economic Studies, 2010, 77 (4): 1540- 1566. doi: 10.1111/j.1467-937X.2010.00608.x
137	Dreber A , Rand D G , Fudenberg D , et al. Winners don't punish[J]. Nature, 2008, 452 (7185): 348- 351. doi: 10.1038/nature06723
138	Wu J J , Zhang B , Zhou Z , et al. Costly punishment does not always increase cooperation[J]. Proceedings of the National Academy of Sciences USA, 2009, 106 (41): 17448- 17451. doi: 10.1073/pnas.0905918106
139	Sigmund K , De Silva H , Traulsen A , et al. Social learning promotes institutions for governing the commons[J]. Nature, 2010, 466 (7308): 861- 863. doi: 10.1038/nature09203
140	Sasaki T , Brännström Å , Dieckmann U , et al. The take-it-or-leave-it option allows small penalties to overcome social dilemmas[J]. Proceedings of the National Academy of Sciences USA, 2012, 109 (40): 1165- 1169.
141	Dong Y , Sasaki T , Zhang B . The competitive advantage of institutional reward[J]. Proceedings of the Royal Society B: Biological Sciences, 2019, 286 (1899): 20190001. doi: 10.1098/rspb.2019.0001
142	Zhang B , Li C , De Silva , et al. The evolution of sanctioning institutions: An experimental approach to the social contract[J]. Experimental Economics, 2014, 17 (2): 285- 303. doi: 10.1007/s10683-013-9367-7
143	Boyd R , Gintis H , Bowles S . Coordinated punishment of defectors sustains cooperation and can proliferate when rare[J]. Science, 2010, 328 (5978): 617- 620. doi: 10.1126/science.1183665
144	Andreoni J , Gee L K . Gun for hire: Delegated enforcement and peer punishment in public goods provision[J]. Journal of Public Economics, 2012, 96 (11-12): 1036- 1046. doi: 10.1016/j.jpubeco.2012.08.003
145	Dong Y , Ma S , Zhang B , et al. Financial incentives for poor countries promote net emissions reductions in multilateral climate agreements[J]. ONE Earth, 2021, 4 (8): 1141- 1149. doi: 10.1016/j.oneear.2021.07.006
56	Li S , Ma S , Wang D , et al. Oxytocin and the punitive hub-dynamic spread of cooperation in human social networks[J]. Journal of Neuroscience, 2022, 42 (30): 5930- 5943. doi: 10.1523/JNEUROSCI.2303-21.2022
57	Nowak M A . Five rules for the evolution of cooperation[J]. Science, 2006, 314 (5805): 1560- 1563. doi: 10.1126/science.1133755
58	Rapoport A . Fights, Games, and Debates[M]. Ann Arbor: University of Michigan Press, 1960.
59	Nowak M A , Sigmund K . The evolution of stochastic strategies in the Prisoner's Dilemma[J]. Acta Applicandae Mathematica, 1990, 20 (3): 247- 265. doi: 10.1007/BF00049570
60	Nowak M A , Sigmund K . Tit for tat in heterogenous populations[J]. Nature, 1992, 355 (6357): 250- 253. doi: 10.1038/355250a0
61	Nowak M A , Sigmund K . A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner's dilemma game[J]. Nature, 1993, 364 (6432): 56- 58. doi: 10.1038/364056a0
62	Hilbe C , Martinez-Vaquero L A , Chatterjee K , et al. Memory-n strategies of direct reciprocity[J]. Proceedings of the National Academy of Sciences USA, 2017, 114 (18): 4715- 4720. doi: 10.1073/pnas.1621239114
63	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 USA, 2012, 109 (26): 10409- 10413. doi: 10.1073/pnas.1206569109
64	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 USA, 2013, 110 (38): 15348- 15353. doi: 10.1073/pnas.1306246110
65	Fudenberg D , Rand D G , Dreber A . Slow to anger and fast to forgive: Cooperation in an uncertain world[J]. The American Economic Review, 2012, 102 (2): 720- 749. doi: 10.1257/aer.102.2.720
66	Hilbe C , Röhl T , Milinski M . Extortion subdues human players but is finally punished in the Prisoner's Dilemma[J]. Nature Communications, 2014, 5 (1): 1- 6.
67	Wang Z , Zhou Y , Lien J W , et al. Extortion can outperform generosity in the iterated prisoner's dilemma[J]. Nature Communications, 2016, 7, 1- 7.
68	Boyd R , Richerson P J . The evolution of reciprocity in sizable groups[J]. Journal of Theoretical Biology, 1988, 132, 337- 356. doi: 10.1016/S0022-5193(88)80219-4
69	Hilbe C , Wu B , Traulsen A , et al. Cooperation and control in multiplayer social dilemmas[J]. Proceedings of the National Academy of Sciences USA, 2014, 111 (46): 16425- 16430. doi: 10.1073/pnas.1407887111
70	Hauser O P , Hilbe C , Chatterjee K , et al. Social dilemmas among unequals[J]. Nature, 2019, 572 (7770): 524- 527. doi: 10.1038/s41586-019-1488-5
71	Hamilton W D . The genetical theory of social behavior, Ⅰ and Ⅱ[J]. Journal of Theoretical Biology, 1964, 7, 1- 52. doi: 10.1016/0022-5193(64)90038-4
72	Levy M , Lo A W . Hamilton's rule in economic decision-making[J]. Proceedings of the National Academy of Sciences USA, 2022, 119 (16): e2108590119. doi: 10.1073/pnas.2108590119
73	Nowak M A , Tarnita C E , Wilson E O . The evolution of eusociality[J]. Nature, 2010, 466 (7310): 1057- 1062. doi: 10.1038/nature09205
74	Dawkins R . The Selfish Gene[M]. Oxford: Oxford University Press, 1976.
75	Traulsen A , Nowak M A . Evolution of cooperation by multilevel selection[J]. Proceedings of the National Academy of Sciences USA, 2006, 103 (29): 10952- 10955. doi: 10.1073/pnas.0602530103
76	Ostrom E . Collective action and the evolution of social norms[J]. The Journal of Economic Perspectives, 2000, 14 (3): 137- 158. doi: 10.1257/jep.14.3.137
77	Wang X , Couto M , Wang N , et al. Cooperation and coordination in heterogeneous populations[J]. Philosophical Transactions of the Royal Society B, 2023, 378 (1876): 20210504. doi: 10.1098/rstb.2021.0504
146	Tirole J . Economics for the Common Good[M]. Princeton: Princeton University Press, 2017.
147	Ariely D , Bracha A , Meier S . Doing good or doing well? Image motivation and monetary incentives in behaving prosocially[J]. The American Economic Review, 2009, 99 (1): 544- 555. doi: 10.1257/aer.99.1.544
148	Bénabou R , Tirole J . Intrinsic and extrinsic motivation[J]. The Review of Economic Studies, 2003, 70 (3): 489- 520. doi: 10.1111/1467-937X.00253
78	Wu J , Li C , Zhang B , et al. The role of institutional incentives and the exemplar in promoting cooperation[J]. Scientific Reports, 2014, 4 (1): 6421. doi: 10.1038/srep06421
79	Fehr E , Fischbacher U . Third-party punishment and social norms[J]. Evolution and Human Behavior, 2004, 25 (2): 63- 87. doi: 10.1016/S1090-5138(04)00005-4

博弈类型	单轮纳什均衡	利他偏好	互惠偏好	公平偏好
囚徒困境博弈	不合作	合作	TFT, GTFT等策略	—
公共品博弈	不贡献	贡献	条件合作	—
最后通牒博弈	不公平分配	回应者接受任何分配	—	回应者拒绝不公平的分配
信任博弈	不信任	委托人将全部财富给代理人	代理人返还部分收益	代理人返还一半收益
个体间奖惩博弈	不使用奖惩	—	—	惩罚不合作者, 奖励合作者

	随机相遇	规则网络	随机网络	无标度网络
生灭过程	不合作	不合作	不合作	不合作
灭生过程	不合作	$ \frac{b}{c}>z $	$ \frac{b}{c}>z $	$ \frac{b}{c}>z $
择优模仿	不合作	不合作	$ \frac{b}{c}>(z-1)(\frac{2z^{2}}{\rm var( \it k)}+1) $	$ \frac{b}{c}>z-1 $
最优反应	不合作	不合作	不合作	不合作
行为实验	不合作	有争议	N/A	不合作

信誉机制类型	评价指标	信誉更新方式	间接互惠策略
形象评分机制	形象评分	合作+1分, 不合作−1分	只与评分不低于$ k $的人合作
二元分类机制	好、坏	与好人合作获得好声誉, 背叛好人声誉变坏	只与好人合作
综合评价机制	好、坏、信誉评分、自身信息	设定好人的分数阈值$ k $, 与好人合作+1分, 背叛好人−1分	自己是好人时与好人合作, 自己是坏人时不合作

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