﻿ 基于演化博弈的合作进化研究综述 Evolution of Cooperation Based on Evolutionary Game: A Comprehensive Review

Management Science and Engineering
Vol.05 No.03(2016), Article ID:18488,14 pages
10.12677/MSE.2016.53013

Evolution of Cooperation Based on Evolutionary Game: A Comprehensive Review

Yaofeng Zhang

School of Statistics, Hubei University of Economics, Wuhan Hubei

Received: Aug. 15th, 2016; accepted: Sep. 1st, 2016; published: Sep. 7th, 2016

ABSTRACT

Evolution of cooperation is an important mechanism in social evolution process. Evolutionary game theory and computer simulation technology provide a new perspective for analyzing cooperative behavior of human. To reflect the research progress of evolution of cooperation, we reviewed literatures of cooperative evolution based on evolutionary game. Firstly, we present several evolutionary game models used in the study of evolution of cooperation. And then, main mechanisms of promoting cooperation level are summarized. Finally, important factors influences the evolution of cooperation are inducted. Based on the review of research status, further analysis on the existed problems and shortcomings is made and some perspectives on the development trends of future research are provided.

Keywords:Evolutionary Game, Evolution of Cooperation, Complex Networks, Simulation

1. 引言

2. 合作进化研究的演化博弈模型

2.1. 囚徒困境博弈

Axelord将互惠利他理论与演化博弈论相结合提出的回报理论 [19] 是以“囚徒困境”博弈(Prisoner’s Dilemma, PD)为基础的。一般形式的“囚徒困境”模型如表1所示，可简要地叙述为：博弈方1和博弈方2只有合作(Cooperation, C)或背叛(Defection, D)两种选择。双方都合作各得；一方合作一方背叛时，合作方得，背叛方得；双方都背叛则各得。在囚徒困境博弈模型中，所有收益满足，并且通常假设

Doebeli和Hauert在文献 [7] 中介绍了最新的基于演化囚徒困境博弈的程序锦标赛，指出一个所谓的“串谋”策略脱颖而出。该策略只对自己的同类合作，而对其他个体采用TFT策略。为了区分同类和非同类，它们在每一轮与其他个体博弈之前都先通过一次秘密的“握手”进行身份认定。虽然该策略在身份认定机制最初如何演化等方面还有待进一步的研究，但是“串谋”的概念为心理学等学科中应用演化囚徒困境博弈研究问题提供了一个崭新的视角。

2.2. 雪堆博弈

SD模型可描述为：两个司机(博弈双方)被困于一个雪堆的两侧，博弈双方有铲雪(Cooperation)和不铲雪(Defection)两种选择。如果双方都铲雪，则各得R收益；如果都不铲雪，则双方的收益均为0；如果其中一方铲雪，另一方不铲，则铲雪方得S，不铲雪方得T。其中，T为顺利回家收益，铲雪会有一定的成本。则一般形式的雪堆博弈收益矩阵如表2所示。

Table 1. The payoff matrix of the prisoner’s dilemma game

Table 2. The snowdrift game payoff matrix

2.3. 公共品博弈

2.4. 石头·剪刀·布博弈

3. 促进合作进化的机制

3.1. 亲缘选择

Table 3. Stone scissors cloth game of gain matrix

3.2. 互惠机制

3.2.1. 直接互惠

Tricers的互惠利他观点体现了这样一种思想，即合作可以在当前收益决定未来行动的机制下产生，上一轮两者博弈的结果作为下一轮博弈所要采取策略的参考。当然这就需要直接互惠要满足一个重要前提，即相同的两个个体要以较大的概率重复相遇。直接互惠的博弈理论模型主要是演化囚徒困境博弈。Axelrod将直接互惠机制与演化博弈论结合 [19] ，为直接互惠理论的研究开辟了道路。在 3.2.1 节中讨论的关于TFT、GTFT以及Pavlov等策略均属于影响直接互惠的策略，这里不再赘述。

3.2.2. 间接互惠

Nowak和Sigmund认为由于在国际市场上一次性的交易越来越多，改变了以往企业间长期的频繁接触 [49] 。例如网上拍卖和电子商务等商业活动中大量存在一次性行为，两个体长期频繁接触的条件不能满足。这种情况下，商业个体之间是否能够合作很大程度上依靠个体的“名誉”以及建立在“名誉”基础上的相互信任。间接互惠不象直接互惠那样要求两个个体经常相遇，而是允许个体随机选择博弈对手。该机制促进合作的核心思想在于给每个个体都赋予“名誉”。Nowak形象地将直接互惠类比为“物物交换”，而把间接互惠中的“名誉”比为“货币” [16] 。拥有“货币”之后，个体就无需再与固定的对手重复接触。个体“名誉”的好坏取决于个体每次和其他对手的博弈历史，并且每个个体的“名誉”在群体中是众所周知的。拥有好的“名誉”意味着在与其他个体接触时，会得到互惠，反之将被“惩罚”。因此个体每次与对手博弈，决定采取某策略前都会考虑该策略对自己“名誉”的影响。与其他种类的生物不同，人类社会中存在大量的没有关系的个体之间的互惠现象，其中的主要原因是由于人类具有的道德情感，以及由此形成的社会规范 [50] 。因此，很多经济学家和社会学家将间接互惠和道德规范的起源联系起来 [49] 。

3.3. 群选择

3.4. 自愿参与

Nowak指出，在囚徒困境博弈中引入自愿参与策略也是促进合作进化的一种机制 [16] 。这里的自愿参与是指参加博弈的个体可以选择合作和背叛，还可以“单干” [60] 。选择单干策略的个体可以暂时不参与博弈，但是仍然可以得到固定的一个小收益。Szabó和Hauert在空间公共基金博弈和进化囚徒困境博弈中引入了单干策略 [61] ，对规则方格子上的研究表明，单干策略的引入可以使原先的博弈转化为了“石头–剪刀–布”类型的博弈 [62] 。吴枝喜在Szabó和Hauert的研究基础上研究了Newman-Watts (NW)小世界网络上自愿参加的空间囚徒困境博弈 [63] ，得到了一些有意义的分析结论。

3.5. 基于“标签”的机制

3.6. 空间结构

4. 影响合作进化的因素

4.1. 贴现系数

4.2. 博弈顺序

4.3. 博弈人数

4.4. 信任

4.5. 惩罚与奖励

4.6. 其他因素

Santos和Pacheco等采用同步更新的策略对无标度网络上的空间纯策略博弈行为进行了研究 [87] ，发现无标度网络更有利于合作行为的产生。因此网络拓扑的异质性也是提升合作水平的一个重要因素。除了网络的异质性对合作行为有影响外，网络的平均度也是影响合作涌现的重要因素之一。TANG等研究了随机图、小世界、无标度3种网络中平均度对合作水平的影响，发现对于每种网络均存在适当的平均度使得合作水平最优 [88] 。另外，Nowak等则指出在有限人口中人口规模太大和太小都不利于合作水平的提升，个体的异质性差别也要适中才能更有效地提升合作水平 [89] 。

5. 总结与展望

1) 现阶段关于合作进化的研究大多停留在仿真模型的完善与探索研究。能够把合作理论应用到实际问题的文献较少，目前只有在企业合作问题方面有所涉及；

2) 虽然已有研究对合作进化的促进机制和影响因素进行了各种讨论，但缺乏统一的理论框架，研究成果相对离散，未建立宏观理论体系；

3) 随着复杂网络的提出，学者将合作进化问题移植到抽象的复杂网络上来，但缺少利用实际人际关系网络数据进行网络建模，从而进行合作进化分析的研究。

1) 在已有理论研究和建模仿真研究的基础上，积极开展结合具体领域、具体问题的应用研究，研究领域包括供应链合作、合作网络、国际政治关系、复杂社会管理等；

2) 总结归纳已有研究成果，设计基于演化博弈理论的合作进化理论框架，从整体上系统的研究合作进化问题，形成独立的理论体系；

3) 结合大数据技术，建立基于大数据的现实人际关系网络模型，从而研究现实网络上的合作进化问题，进一步深入揭示人类合作进化的内在机理和演化机制。

Evolution of Cooperation Based on Evolutionary Game: A Comprehensive Review[J]. 管理科学与工程, 2016, 05(03): 113-126. http://dx.doi.org/10.12677/MSE.2016.53013

1. 1. 罗伯特•艾克斯罗德, 著.对策中的制胜之道——合作的进化[M]. 吴坚忠, 译. 上海: 上海人民出版社, 1996.

2. 2. Wilkison, G.S. (1984) Reciprocal Food Sharing in the Vampire Bat. Nature, 308, 181-184. http://dx.doi.org/10.1038/308181a0

3. 3. Janzen, D.H. (1979) How to Be a Fig. Annual Review of Ecology and Systematics, 10, 13-51. http://dx.doi.org/10.1146/annurev.es.10.110179.000305

4. 4. Crespi, B.J. and Choe, J.C. (1997) The Evolution of Social Behavior in Insects and Arachnids. Cambridge University Press,Cambridge.

5. 5. Ostrom, E., Burger, J., Field, C.B., Norgaard, R.B. and Policansky, D. (1999) Revisiting the Commons: Local Lessons, Global Challenges. Science, 284, 278-282. http://dx.doi.org/10.1126/science.284.5412.278

6. 6. Fehr, E. and Fischbacher, U. (2003) The Nature of Human Altruism. Nature, 425, 785-791. http://dx.doi.org/10.1038/nature02043

7. 7. Doebeli, M. and Hauert, C. (2005) Models of Cooperation Based on the Prisoner’s Dilemma and the Snowdrift Game. Ecology Letters, 8, 748-766. http://dx.doi.org/10.1111/j.1461-0248.2005.00773.x

8. 8. Von Neumann, J. and Morgenstern, O. (1944) Theory of Games and Economic Behavior. Princeton University Press, Princeton.

9. 9. Nash, J. (1950) The Bargaining Problem. Econometrica, 18, 155-162. http://dx.doi.org/10.2307/1907266

10. 10. Hofbauer, J. and Sigmund, K. (1998) Evolutionary Games and Population Dynamics. University Press,Cambridge. http://dx.doi.org/10.1017/CBO9781139173179

11. 11. Cressman, R. (2003) Evolutionary Dynamics and Extensive form Games. MIT Press, Cambridge.

12. 12. Colman, A.M. (1995) Game Theory and Its Applications in the Social and Biological Sciences. Butterworth- Heinemann, Oxford.

13. 13. Binmore, K.G. (1994) Playing Fair: Game Theory and the Social Contract. MIT Press, Cambridge.

14. 14. Smith, J.M. and Price, G.R. (1973) The Logic of Animal Conflict. Nature, 246, 15-18. http://dx.doi.org/10.1038/246015a0

15. 15. Nowak, M.A. and Sigmund, K. (2004) Evolutionary Dynamics of Biological Games. Science, 303, 793-799. http://dx.doi.org/10.1126/science.1093411

16. 16. Nowak, M.A. (2006) Five Rules for the Evolution. Science, 314, 1560-1563. http://dx.doi.org/10.1126/science.1133755

17. 17. Hauert, C. and Szabó, G. (2005) Game Theory and Physics. American Journal of Physics, 73, 405-414. http://dx.doi.org/10.1119/1.1848514

18. 18. Trivers, R.L. (1971) The Evolution of Reciprocal Altruism. Quarterly Review of Biology, 46, 35-57. http://dx.doi.org/10.1086/406755

19. 19. Axelrod, R. and Hamilton, W.D. (1981) The Evolution of Cooperation. Science, 211, 1390-1396. http://dx.doi.org/10.1126/science.7466396

20. 20. Dawes, R.M. (1980) Social Dilemmas. Annual Review of Psychology, 31, 169-193. http://dx.doi.org/10.1146/annurev.ps.31.020180.001125

21. 21. McNamara, J.M., Barta, Z. and Houston, A.I. (2004) Variation in Behavior Promotes Cooperation in the Prisoner’s Dilemma Game. Nature, 428, 745-748. http://dx.doi.org/10.1038/nature02432

22. 22. Neill, D.B. (2001) Optimality under Noise, Higher Memory Strategies for the Alternating Prisoner’s Dilemma. Journal of Theoretical Biology, 211, 159-180. http://dx.doi.org/10.1006/jtbi.2001.2337

23. 23. Killingback, T., Doebeli, M. and Knowlton, N. (1999) Variable Investment, the Continuous Prisoner’s Dilemma, and the Origin of Cooperation. Proceedings of the Royal Society of London B, 266, 1723-1728. http://dx.doi.org/10.1098/rspb.1999.0838

24. 24. Masuda, N. and Aihara, K. (2003) Spatial Prisoner’s Dilemma Optimally Played in Small-World Networks. Physics Letters A, 313, 55-61. http://dx.doi.org/10.1016/S0375-9601(03)00693-5

25. 25. Nowak, M.A. and Sigmund, K. (2004) Evolutionary Dynamics of Biological Games. Science, 303, 793-799. http://dx.doi.org/10.1126/science.1093411

26. 26. Ishibuchi, H. and Namikawa, N. (2005) Evolution of Iterated Prisoner’s Dilemma Game Strategies in Structured Demes under Random Pairing in Game-Playing. IEEE Transactions on Evolutionary Computation, 9, 552-561. http://dx.doi.org/10.1109/TEVC.2005.856198

27. 27. Scheuring, I. (2005) The Iterated Continuous Prisoner’s Dilemma Game Cannot Explain the Evolution of Interspecific Mutualism in Unstructured Populations. Journal of Theoretical Biology, 232, 99-104. http://dx.doi.org/10.1016/j.jtbi.2004.07.025

28. 28. Nowak, M.A. and Sigmund, K. (1992) Tit-for-Tat in Heterogeneous Populations. Nature, 355, 250-253. http://dx.doi.org/10.1038/355250a0

29. 29. Nowak, M.A. and Sigmund, K. (1990) The Evolution of Stochastic Strategies in the Prisoner’s Dilemma. Acta Applicandae Mathematicae, 20, 247-265. http://dx.doi.org/10.1007/BF00049570

30. 30. Boyd, R. and Lorberbaum, J.M.D. (1987) No Pure Strategy Is Evolutionary Stable in the Iterated Prisoner’s Dilemma Game. Nature, 327, 58-59. http://dx.doi.org/10.1038/327058a0

31. 31. Nowak, M.A. and Sigmund, K. (1993) A Strategy of Win-Stay, Lose Shift That Outperforms Tit-for-Tat in the Prisoner’s Dilemma Game. Nature, 364, 56-58. http://dx.doi.org/10.1038/364056a0

32. 32. Nowak, M.A. and Sigmund, K. (1994) The Alternating Prisoner’s Dilemma. Journal of Theoretical Biology, 168, 219- 226. http://dx.doi.org/10.1006/jtbi.1994.1101

33. 33. Kraines, D.P. and Kraines, V.Y. (2000) Natural Selection of Memory-One Strategies for the Iterated Prisoner’s Dilemma. Journal of Theoretical Biology, 203, 335-355. http://dx.doi.org/10.1006/jtbi.2000.1089

34. 34. Maynard Smith, J. (1982) Evolution and the Theory of Games. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511806292

35. 35. Sugden, R. (1986) The Economics of Rights, Cooperation and Welfare. Blackwell, Cornwall.

36. 36. Dubois, F. and Giraldeau, L. (2003) The Forager’s Dilemma: Food Sharing and Food Defense as Risk-Sensitive Foraging Options. American Naturalist, 162, 768-779. http://dx.doi.org/10.1086/379202

37. 37. Posch, M., Pichler, A. and Sigmund, K. (1999) The Efficiency of Adapting Aspiration Levels. Proceedings of the Royal Society of London B, 266, 1427-1435. http://dx.doi.org/10.1098/rspb.1999.0797

38. 38. McElreath, R. (2003) Reputation and the Evolution of Conflict. Journal of Theoretical Biology, 220, 345-357. http://dx.doi.org/10.1006/jtbi.2003.3166

39. 39. Hauert, C. and Doebeli, M. (2004) Spatial Structure Often Inhibits the Evolution of Cooperation in the Snowdrift Game. Nature, 428, 643-646. http://dx.doi.org/10.1038/nature02360

40. 40. Shang, L.H., Li, X. and Wang, X.F. (2006) Cooperative Dynamics of Snowdrift Game on Spatial Distance-Dependent Small-World Networks. European Physical Journal B, 54, 369-373. http://dx.doi.org/10.1140/epjb/e2006-00454-8

41. 41. Hardin, G. (1968) The trAgedy of the Commons. Science, 162, 1243-1248. http://dx.doi.org/10.1126/science.162.3859.1243

42. 42. Hauert, C., Monte, S.D., Hofbauer, J. and Sigmund, K. (2002) Replicator Dynamics for Optional Public Good Games. Journal of Theoretical Biology, 218, 187-194. http://dx.doi.org/10.1006/jtbi.2002.3067

43. 43. 谢识予. 经济博弈论[M]. 第二版. 上海: 复旦大学出版社, 2002.

44. 44. Hamilton, W.D. (1964) The Genetical Evolution of Social Behavior. I. Journal of Theoretical Biology, 7, 1-16. http://dx.doi.org/10.1016/0022-5193(64)90038-4

45. 45. Dawkins, R. (1976) The Selfish Gene. Oxford University Press, Oxford.

46. 46. Dawkins, R. (1979) Twelve Misunderstandings of Kin Selection. Zeitschrift für Tierpsychologie, 51, 184-200.

47. 47. Wilson, E.O. (2005) Kin Selection as the Key to Altruism: Its Rise and Fall. Social Research, 72, 159-168.

48. 48. Nowak, M.A. and Sigmund, K. (1998) Evolution of Indirect Reciprocity by Image Scoring. Nature, 393, 573-577. http://dx.doi.org/10.1038/31225

49. 49. Nowak, M.A. and Sigmund, K. (2005) Evolution of Indirect Reciprocity. Nature, 437, 1291-1298. http://dx.doi.org/10.1038/nature04131

50. 50. Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E. and Gintis, H. (2001) Cooperation, Reciprocity and Punishment in Fifteen Small-Scale Societies. American Economic Review, 91, 73-78. http://dx.doi.org/10.1257/aer.91.2.73

51. 51. Leimar, O. and Hammerstein, P. (2001) Evolution of Cooperation through Indirect Reciprocity. Proceedings of the Royal Society of London B, 268, 745-753. http://dx.doi.org/10.1098/rspb.2000.1573

52. 52. Milinski, M., Semmann, D., Bakker, T.C.M. and Krambeck, H.J. (2001) Cooperation through Indirect Reciprocity: Image Scoring or Standing Strategy? Proceedings of the Royal Society of London B, 268, 2495-2501. http://dx.doi.org/10.1098/rspb.2001.1809

53. 53. 侯云章, 盛昭瀚, 王晓灵, 陈国华. 复杂网络中基于记忆长度的合作行为[J]. 系统工程理论与实践, 2008, 28(2): 119-124.

54. 54. Sigmund, K., Hauert, C. and Nowak, M.A. (2001) Reward and Punishment. Proceedings of the National Academy of Sciences of the United States of America, 98, 10757-10762. http://dx.doi.org/10.1073/pnas.161155698

55. 55. Brandt, H., Hauert, C. and Sigmund, K. (2003) Cooperation, Punishment and Reputation in Spatial Games. Proceedings of the Royal Society of London B, 270, 1099-1104. http://dx.doi.org/10.1098/rspb.2003.2336

56. 56. Traulsen, A. and Nowak, M.A. (2006) Evolution of Cooperation by Multilevel Selection. Proceedings of the National Academy of Sciences of the United States of America, 103, 10952-10955. http://dx.doi.org/10.1073/pnas.0602530103

57. 57. 张四海. 基于社会网络和博弈论的合作理论研究[D]: [博士学位论文]. 合肥: 中国科技大学, 2006.

58. 58. Thompson, N.S. (2000) Shifting the Natural Selection Metaphor to the Group Level. Behavior and Philosophy, 28, 83-101.

59. 59. Foster, K.R., Wenseleers, T. and Ratnieks, F.L.W. (2006) Kin Selection Is the Key to Altruism. Trends in Ecology and Evolution, 21, 57-60. http://dx.doi.org/10.1016/j.tree.2005.11.020

60. 60. Hauert, C., De Monte, S., Hofbauer, J. and Sigmund, K. (2002) Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games. Science, 296, 1129-1132. http://dx.doi.org/10.1126/science.1070582

61. 61. Szabó, G. and Hauert, C. (2002) Evolutionary Prisoner’s Dilemma Games with Voluntary Participation. Physical Review E, 66, Article ID: 062903. http://dx.doi.org/10.1103/physreve.66.062903

62. 62. Semmann, D., Krambeck, H.J. and Milinski, M. (2003) Volunteering Leads to Rock-Paper-Scissors Dynamics in a Public Goods Game. Nature, 425, 390-393. http://dx.doi.org/10.1038/nature01986

63. 63. 吴枝喜. 复杂网络及其上的进化博弈研究[D]: [博士学位论文]. 兰州: 兰州大学, 2007.

64. 64. Riolo, R.L., Cohen, M.D. and Axelrod, R. (2001) Evolution of Cooperation without Reciprocity. Nature, 414, 441-443. http://dx.doi.org/10.1038/35106555

65. 65. Roberts, G. and Sherratt, T.N. (2002) Does Similarity Breed Cooperation? Nature, 418, 499-500. http://dx.doi.org/10.1038/418499b

66. 66. Axelrod, R., Hammond, R.A. and Grafen, A. (2004) Altruism via Kin-Selection Strategies That Rely on Arbitrary Tags with Which They Coevolve. Evolution, 58, 1833-1838. http://dx.doi.org/10.1111/j.0014-3820.2004.tb00465.x

67. 67. Nowak, M.A. and May, R.M. (1992) Evolutionary Games and Spatial Chaos. Nature, 359, 826-829. http://dx.doi.org/10.1038/359826a0

68. 68. Nowak, M.A. and May, R.M. (1993) The Spatial Dilemmas of Evolution. International Journal of Bifurcation and Chaos, 3, 35-78. http://dx.doi.org/10.1142/S0218127493000040

69. 69. Szabó, G. and Töke, C. (1998) Evolutionary Prisoner’s Dilemma Game on a Square Lattice. Physical Review E, 58, 69-73. http://dx.doi.org/10.1103/PhysRevE.58.69

70. 70. Szabó, G. and Töke, C. (2002) Phase Transitions and Volunteering in Spatial Public Goods Games. Physical Review Letters, 89, Article ID: 118101. http://dx.doi.org/10.1103/physrevlett.89.118101

71. 71. Szabó, G., Antal, T., Szabo, P. and Droz, M. (2000) Spatial Evolutionary Prisoner’s Dilemma Game with Three Strategies and External Constraints. Physical Review E, 62, 1095-1103. http://dx.doi.org/10.1103/PhysRevE.62.1095

72. 72. Watts, D.J. and Strogatz, S.H. (1998) Collective Dynamics of “Small-World” Networks. Nature, 393, 440-442.. http://dx.doi.org/10.1038/30918

73. 73. Barabási, A.L. and Albert, R. (1999) Emergence of Scaling in Random Networks. Science, 286, 509-512. http://dx.doi.org/10.1126/science.286.5439.509

74. 74. Abramson, G. and Kuperman, M. (2001) Social Games in a Social Network. Physical Review E, 63, Article ID: 030901. http://dx.doi.org/10.1103/physreve.63.030901

75. 75. 王龙, 伏锋, 陈小杰, 王靖, 李卓政, 谢广明, 楚天广. 复杂网络上的演化博弈[J]. 智能系统学报, 2007, 2(2): 1-10.

76. 76. 赵晟莹, 郭强, 王文旭, 任杰, 刘建国. 复杂网络上博弈行为的研究进展[J]. 电子测量技术. 2007, 30(4): 93-96.

77. 77. Stephens, D.W., Mclinn, C.M. and Stevens, J.R. (2002) Discounting and Reciprocity in an Iterated Prisoner’s Dilemma. Science, 298, 2216-2218. http://dx.doi.org/10.1126/science.1078498

78. 78. Frean, M.R. (1994) The Prisoner’s Dilemma without Synchrony. Proceedings of the Royal Society B, 257, 75-79. http://dx.doi.org/10.1098/rspb.1994.0096

79. 79. Hauert, C.H. and Schuster, H.G. (1998) Extending the Iterated Prisoner’s Dilemma without Synchrony. Journal of Theoretical Biology, 192, 155-166. http://dx.doi.org/10.1006/jtbi.1997.0590

80. 80. Mataushima, M. and Ikegami, T. (1998) Evolution of Strategies in the Three-Person Iterate Prisoner’s Dilemma. Journal of Theoretical Biology, 195, 53-67. http://dx.doi.org/10.1006/jtbi.1998.0780

81. 81. Yao, X. and Darwen, P. (1994) An Experimental Study of N-Person Iterated Prisoner’s Dilemma Games. Informatica, 18, 435-450.

82. 82. Seo, Y.G. and Cho, S.B. (1999) An Evolutionary Study on Cooperation in N-Person Iterated Prisoner’s Dilemma Game. 2nd Asia-Pacific Conference on Simulated Evolution and Learning, Canberra, 24-27 November 1998, 301-308. http://dx.doi.org/10.1007/3-540-48873-1_39

83. 83. Morgan, R.M. and Hunt, S.D. (1997) The Commitment-Trust Theory of Relationship Marketing. Journal of Marketing, 58, 20-38. http://dx.doi.org/10.2307/1252308

84. 84. Spekman, R.E., Isabella, L.A. and Macavor, T.C. (1998) Alliances Management: A View from Past and a Look to the Future. Journal of Management Studies, 35, 747-772. http://dx.doi.org/10.1111/1467-6486.00118

85. 85. Giniis, H. and Bowles, S. (2004) The Evolution of Strong Reciprocity: Cooperation in Heterogeneous Populations. Theoretical Population Biology, 65, 17-28. http://dx.doi.org/10.1016/j.tpb.2003.07.001

86. 86. Henrieh, J. and Boyd, R. (2001) Why People Punish Defectors: Weak Conformist Transmission Can Stabilize Costly Enforcement of Norms in Cooperative Dilemmas. Journal of Theoretical Biology, 208, 79-89. http://dx.doi.org/10.1006/jtbi.2000.2202

87. 87. Santos, F.C. and Pacheco, J.M. (2005) Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation. Physical Review Letters, 95, Article ID: 098104. http://dx.doi.org/10.1103/physrevlett.95.098104

88. 88. Tang, C.L., Wang, W.X., Wu, X. and Wang, B.H. (2006) Effect of Average Degree on Cooperation in Networked Evolutionary Game. European Physical Journal B, 53, 411-415. http://dx.doi.org/10.1140/epjb/e2006-00395-2

89. 89. Nowak, M.A., Sasaki, A., Taylor, C. and Fuden-Berg, D. (2004) Emergence of Cooperation and Evolutionary Stability in Finite Populations. Nature, 428, 646-650. http://dx.doi.org/10.1038/nature02414

90. 90. Scott, J. (2000) Social Network Analysis. 2nd Edition, Sage, London.

91. 91. Newman, M.E.J. (2002) Assortative Mixing in Networks. Physical Review Letters, 89, Article ID: 208701. http://dx.doi.org/10.1103/physrevlett.89.208701

92. 92. Newman, M.E.J. (2006) The Structure and Function of Complex Networks. SIAM Review, 45, 167-256. http://dx.doi.org/10.1137/S003614450342480