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Game Theory and the Evolution of Cooperation

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Abstract

Evolution is based on the competition between individuals and therefore rewards only selfish behavior. How cooperation or altruism behavior could prevail in social dilemma then becomes a problematic issue. Game theory offers a powerful mathematical approach for studying social behavior. It has been widely used to explain the evolution of cooperation. In this paper, we first introduce related static and dynamic game methods. Then we review two types of mechanisms that can promote cooperation in groups of genetically unrelated individuals, (i) direct reciprocity in repeated games, and (ii) incentive mechanisms such as reward and punishment.

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References

  1. Pennisi, E.: How did cooperative behavior evolve? Science 309(5731), 93–93 (2005)

    Google Scholar 

  2. Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)

    MATH  Google Scholar 

  3. Nowak, M.A.: Evolutionary Dynamics. Belknap Press, Cambridge (2006)

    MATH  Google Scholar 

  4. Sigmund, K.: The Calculus of Selfishness. Princeton University Press, Princeton (2010)

    MATH  Google Scholar 

  5. Nash, J.: Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 36, 48–49 (1950)

    MathSciNet  MATH  Google Scholar 

  6. Harsanyi, J.C., Selten, R.: A general theory of equilibrium selection in games. MIT Press, Cambridge (1988)

    MATH  Google Scholar 

  7. Maynard Smith, J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  8. Maynard Smith, J.M., Price, G.R.: The logic of animal conflict. Nature 246(5427), 15–18 (1973)

    MATH  Google Scholar 

  9. McKelvey, R.D., Palfrey, T.A.: Quantal response equilibria for normal form games. Games Econ. Behav. 10, 6–38 (1995)

    MathSciNet  MATH  Google Scholar 

  10. Goeree, J.K., Holt, C.A., Palfrey, T.A.: Regular quantal response equilibrium. Exp. Econ. 8, 347–367 (2005)

    MATH  Google Scholar 

  11. McKelvey, R.D., Palfrey, T.A.: Quantal response equilibria for extensive form games. Exp. Econ. 1, 9–41 (1998)

    MATH  Google Scholar 

  12. Sandholm, W.H.: Population Games and Evolutionary Dynamics. MIT Press, Cambridge (2010)

    MATH  Google Scholar 

  13. Turocy, T.L.: A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence. Games Econ. Behav. 51, 243–263 (2005)

    MathSciNet  MATH  Google Scholar 

  14. Zhang, B., Fan, S., Li, C., Zheng, X., Bao, J., Cressman, R., Tao, Y.: Opting out against defection leads to stable coexistence with cooperation. Sci. Rep. 6, 35902 (2016). https://doi.org/10.1038/srep35902

    Google Scholar 

  15. Zhang, B.: Quantal response methods for equilibrium selection in normal form game. J. Math. Econ. 64, 113–123 (2016)

    MathSciNet  MATH  Google Scholar 

  16. Zhang, B., Hofbauer, J.: Quantal response methods for equilibrium selection in 2×2 coordination games. Games Econ. Behav. 97, 19–31 (2016)

    MathSciNet  MATH  Google Scholar 

  17. Hofbauer, J., Sigmund, K.: Evolutionary games and population dynamics. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  18. Taylor, P., Jonker, L.: Evolutionary stable strategies and game dynamics. Math. Biosci. 50, 145–156 (1978)

    MATH  Google Scholar 

  19. Börgers, T., Sarin, R.: Learning through reinforcement and replicator dynamics[J]. J. Econ. Theory 77(1), 1–14 (1997)

    MathSciNet  MATH  Google Scholar 

  20. Schlag, K.H.: Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits. J. Econ. Theory 78(1), 130–156 (1998)

    MathSciNet  MATH  Google Scholar 

  21. Weibull, J.W.: Evolutionary Game Theory. MIT press, Cambridge (1995)

    MATH  Google Scholar 

  22. Samuelson, L.: Evolutionary Games and Equilibrium Selection. MIT press, Boston (1997)

    MATH  Google Scholar 

  23. Binmore, K., Samuelson, L.: Muddling through: noisy equilibrium selection. J. Econ. Theory 74(2), 235–265 (1997)

    MathSciNet  MATH  Google Scholar 

  24. Cressman, R.: The Stability Concept of Evolutionary Game Theory: A Dynamic Approach. Springer, Berlin (1992)

    MATH  Google Scholar 

  25. Hofbauer, J., Schuster, P., Sigmund, K.: A note on evolutionary stable strategies and game dynamics. J. Theor. Biol. 81(3), 609–612 (1979)

    MathSciNet  Google Scholar 

  26. Zeeman, E.C.: Population Dynamics from Game Theory/Global Theory of Dynamical Systems, pp. 471–497. Springer, Berlin (1980)

    Google Scholar 

  27. Cressman, R., Ansell, C., Binmore, K.: Evolutionary Dynamics and Extensive form Games, vol. 5. MIT Press, Cambridge (2003)

    Google Scholar 

  28. Maynard Smith, J., Hofbauer, J.: The “battle of the sexes”: a genetic model with limit cycle behavior. Theor. Popul. Biol. 32(1), 1–14 (1987)

    MathSciNet  MATH  Google Scholar 

  29. Schuster, P., Sigmund, K.: Coyness, philandering and stable strategies. Anim. Behav. 29(1), 186–192 (1981)

    Google Scholar 

  30. Selten, R.: A note on evolutionarily stable strategies in asymmetric animal conflicts. J. Theor. Biol. 84, 93–101 (1980)

    MathSciNet  Google Scholar 

  31. Zhang, B., Hofbauer, J.: Equilibrium selection via replicator dynamics. Int. J. Game Theory 44, 433–448 (2015)

    MATH  Google Scholar 

  32. Eshel, I.: Evolutionarily stable strategies and viability selection in Mendelian populations. Theor. Popul. Biol. 22(2), 204–217 (1982)

    MathSciNet  MATH  Google Scholar 

  33. Lessard, S.: Evolutionary dynamics in frequency-dependent two-phenotype models. Theor. Popul. Biol. 25(2), 210–234 (1984)

    MathSciNet  MATH  Google Scholar 

  34. Maynard Smith, J.: Will a sexual population evolve to an ESS? [J]. Am. Nat. 117(6), 1015–1018 (1981)

    Google Scholar 

  35. Axelrod, R., Hamilton, W.D.: The evolution of cooperation. Science 211, 1390–1396 (1981)

    MathSciNet  MATH  Google Scholar 

  36. Milinski, M.: Tit for tat in sticklebacks and the evolution of cooperation. Nature 325, 433–435 (1987)

    Google Scholar 

  37. Adami, C., Hintze, A.: Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything. Nat. Commun. 4, 2193 (2013)

    Google Scholar 

  38. Hilbe, C., Nowak, M.A., Sigmund, K.: The evolution of extortion in iterated prisoner’s dilemma games. Proc. Natl. Acad. Sci. USA 110, 6913–6918 (2013)

    MathSciNet  MATH  Google Scholar 

  39. Nowak, M.A., Sigmund, K.: The evolution of stochastic strategies in the Prisoner’s Dilemma. Acta Appl. Math. 20, 247–265 (1990)

    MathSciNet  MATH  Google Scholar 

  40. Nowak, M.A., Sigmund, K.: Tit for tat in heterogeneous populations. Nature 355, 250–253 (1992)

    Google Scholar 

  41. Nowak, M.A., Sigmund, K.: A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner’s Dilemma game. Nature 364, 56–58 (1993)

    Google Scholar 

  42. Press, W.H., Dyson, F.D.: Iterated prisoner’s dilemma contains strategies that dominate any evolutionary opponent. Proc. Natl. Acad. Sci. USA 109, 10409–10413 (2012)

    MATH  Google Scholar 

  43. Stewart, A.J., Plotkin, J.B.: From extortion to generosity, evolution in the iterated prisoner’s dilemma. Proc. Natl. Acad. Sci. USA 110, 15348–15353 (2013)

    MathSciNet  MATH  Google Scholar 

  44. Fudenberg, D., Harris, C.: Evolutionary dynamics with aggregate shocks. J. Econ. Theor. 57, 420–441 (1992)

    MathSciNet  MATH  Google Scholar 

  45. Imhof, L.A., Fudenberg, D., Nowak, M.A.: Evolutionary cycles of cooperation and defection. Proc. Natl. Acad. Sci. USA 102, 10797–10800 (2005)

    Google Scholar 

  46. Kurokawa, S., Ihara, Y.: Emergence of cooperation in public goods games. Proc. R. Soc. B. 276, 1379–1384 (2009)

    Google Scholar 

  47. Nowak, M.A., Sasaki, A., Taylor, C., Fudenberg, D.: Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)

    Google Scholar 

  48. Dong, Y., Li, C., Tao, Y., Zhang, B.: Evolution of conformity in social dilemmas. PLoS ONE 10, e0137435 (2015). https://doi.org/10.1371/journal.pone.0137435

    Google Scholar 

  49. Hilbe, C., Röhl, T., Milinski, M.: Extortion subdues human players but is finally punished in the prisoner’s dilemma. Nat. Commun. 5, 3976 (2014)

    Google Scholar 

  50. Wang, Z., Zhou, Y., Lien, J.W., Zheng, J., Xu, B.: Extortion can outperform generosity in the iterated prisoners’ dilemma. Nat. Commu. 7, 11125 (2016)

    Google Scholar 

  51. Le, S., Boyd, R.: Evolutionary dynamics of the continuous iterated Prisoner’s Dilemma. J. Theor. Biol. 245, 258–267 (2007)

    MathSciNet  MATH  Google Scholar 

  52. Wahl, L., Nowak, M.A.: The continuous Prisoner’s Dilemma: I. linear reactive strategies. J. Theor. Biol. 200, 307–321 (1999)

    Google Scholar 

  53. Wahl, L., Nowak, M.A.: The continuous Prisoner’s Dilemma: II. Linear reactive strategies with noise. J. Theor. Biol. 200, 323–338 (1999)

    Google Scholar 

  54. Boyd, R., Richerson, P.J.: The evolution of reciprocity in sizable groups. J. Theor. Biol. 132, 337–356 (1988)

    MathSciNet  Google Scholar 

  55. Hauert, C., Schuster, H.: Effects of increasing the number of players and memory size in the iterated Prisoner’s Dilemma: a numerical approach. Proc. R. Soc. B. 264, 513–519 (1997)

    Google Scholar 

  56. Pinheiro, F.L., Vasconcelos, V.V., Santos, F.C., Pacheco, J.M.: Evolution of all-or-none strategies in repeated public goods dilemmas. PLoS Comput. Biol. 10, e1003945 (2014)

    Google Scholar 

  57. Gracia-Lázaro, C., Ferrer, A., Ruiz, G., Tarancón, A., Cuesta, J.A., Sánchez, A., et al.: Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma. Proc. Natl. Acad. Sci. USA 109, 12922–12926 (2012)

    Google Scholar 

  58. Grujić, J., Fosco, C., Araujo, L., Cuesta, J.A., Sánchez, A.: Social experiments in the mesoscale: humans playing a spatial Prisoner’s Dilemma. PLoS ONE 5, e13749 (2010). https://doi.org/10.1371/journal.pone.0013749

    Google Scholar 

  59. Grujić, J., Gracia-Lázaro, C., Milinski, M., Semmann, D., Traulsen, A., Cuesta, J.A., et al.: A comparative analysis of spatial Prisoners Dilemma experiments: conditional cooperation and payoff irrelevance. Sci. Rep. 4, 4615 (2014)

    Google Scholar 

  60. Grujić, J., Röhl, T., Semmann, D., Milinski, M., Traulsen, A.: Consistent strategy updating in spatial and nonspatial behavioral experiments does not promote cooperation in social networks. PLoS ONE 7, e47718 (2012). https://doi.org/10.1371/journal.pone.0047718

    Google Scholar 

  61. Traulsen, A., Semmann, D., Sommerfeld, R.D., Krambeck, H.J., Milinski, M.: Human strategy updating in evolutionary games. Proc. Natl. Acad. Sci. USA 107, 2962–2966 (2010)

    Google Scholar 

  62. Fischbacher, U., Gächter, S.: Social preferences, beliefs, and the dynamics of free riding in public goods experiments. Am. Econ. Rev. 100, 541–556 (2010)

    Google Scholar 

  63. Fischbacher, U., Gächter, S., Fehr, E.: Are people conditionally cooperative? Evidence from a public goods experiment. Econ. Lett. 71, 397–404 (2001)

    MATH  Google Scholar 

  64. Keser, C., van Winden, F.: Conditional cooperation and voluntary contributions to public goods. Scand. J. Econ. 102, 23–39 (2000)

    Google Scholar 

  65. Kurzban, R., Houser, D.: Experiments investigating cooperative type in humans: a complement to evolutionary theory and simulations. Proc. Natl. Acad. Sci. USA 102, 1803–1807 (2005)

    Google Scholar 

  66. Wu, J.J., Li, C., Zhang, B., Cressman, R., Tao, Y.: The role of institutional incentives and the exemplar in promoting cooperation. Sci. Rep. 4, 6421 (2014)

    Google Scholar 

  67. Axelrod, R., Dion, D.: The further evolution of cooperation. Science 242, 1385–1390 (1988)

    Google Scholar 

  68. Nowak, M.A.: Five rules for the evolution of cooperation. Science 314(5805), 1560–1563 (2006)

    Google Scholar 

  69. Aktipis, C.A.: Know when to walk away: contingent movement and the evolution of cooperation. J. Theor. Biol. 231, 249–260 (2004)

    MATH  Google Scholar 

  70. Fujiwara-Greve, T., Okuno-Fujiwara, M.: Voluntarily separable repeated prisoner’s dilemma. Rev. Econ. Stud. 76, 993–1021 (2009)

    MathSciNet  MATH  Google Scholar 

  71. Hauk, E.: Multiple prisoner’s dilemma games with (out) an outside option: an experimental study. Theory Decis. 54(3), 207–229 (2003)

    MathSciNet  MATH  Google Scholar 

  72. Hayashi, N.: From TIT-for-TAT to OUT-for-TAT. Soc. Theory Methods 8, 19–32 (1993)

    Google Scholar 

  73. Izquierdo, S.S., Izquierdo, L.R., Vega-Redondo, F.: The option to leave: conditional dissociation in the evolution of cooperation. J. Teor. Biol. 267, 76–84 (2010)

    MathSciNet  MATH  Google Scholar 

  74. Orbell, J.M., Dawes, R.M.: Social welfare, cooperators’ advantage, and the option of not playing the game. Am. Sociol. Rev. 58, 787–800 (1993)

    Google Scholar 

  75. Schuessler, R.: Exit threats and cooperation under anonymity. J. Conflict Resolut. 33, 728–749 (1989)

    Google Scholar 

  76. Zheng, X.D., Li, C., Yu, J.R., Wang, S.C., Fan, S.J., Zhang, B.Y., Tao, Y.: A simple rule of direct reciprocity leads to the stable coexistence of cooperation and defection in the prisoner’s dilemma game. J. Theor. Biol. 420, 12–17 (2017)

    MathSciNet  MATH  Google Scholar 

  77. Hauert, C., De Monte, S., Hofauer, J., Sigmund, K.: Volunteering as red queen mechanism for cooperation in public goods games. Science 296, 1129–1132 (2002)

    Google Scholar 

  78. Semmann, D., Krambeck, H.J., Milinski, M.: Volunteering leads to rock–paper–scissors dynamics in a public goods game. Nature 425, 390–393 (2003)

    Google Scholar 

  79. Hamilton, W.D.: The genetical evolution of social behaviour I. J. Theor. Biol. 7, 1–52 (1964)

    Google Scholar 

  80. Trivers, R.L.: The evolution of reciprocal altruism. Q. Rev. Biol. 46, 35–57 (1971)

    Google Scholar 

  81. Clutton-Brock, T.H., Parker, G.A.: Punishment in animal societies. Nature 373, 209–216 (1995)

    Google Scholar 

  82. Balliet, D., Mulder, L.B., VanLange, P.A.M.: Reward, punishment, and cooperation: a meta-analysis. Psychol. Bull. 137, 594–615 (2011)

    Google Scholar 

  83. Guala, F.: Reciprocity: weak or strong? What punishment experiments do (and do not) demonstrate. Behav. Brain Sci. 35, 1–15 (2012)

    Google Scholar 

  84. Perc, M., Jordan, J.J., Rand, D.G., Wang, Z., Boccaletti, S., Szolnoki, A.: Statistical physics of human cooperation. Phys. Rep. 687, 1–51 (2017)

    MathSciNet  MATH  Google Scholar 

  85. Hilbe, C., Sigmund, K.: Incentives and opportunism: from the carrot to the stick. Proc. R. Soc. B 277, 2427–2433 (2010)

    Google Scholar 

  86. Sigmund, K., Hauert, C., Nowak, M.A.: Reward and punishment. Proc. Natl Acad. Sci. USA 98(10), 757–10762 (2001)

    Google Scholar 

  87. Boyd, R., Gintis, H., Bowles, S., Richerson, P.J.: The evolution of altruistic punishment. Proc. Natl Acad. Sci. USA 100, 3531–3535 (2003)

    Google Scholar 

  88. dos Santos, M.: The evolution of anti-social rewarding and its countermeasures in public goods games. Proc. R. Soc. B 282 (2015). https://doi.org/10.1098/rspb.2014.1994

    Google Scholar 

  89. Fowler, J.H.: Altruistic punishment and the origin of cooperation. Proc. Natl Acad. Sci. USA 102, 7047–7049 (2005)

    Google Scholar 

  90. Gao, L., Wang, Z., Pansini, R., Li, Y.T., Wang, R.W.: Collective punishment is more effective than collective reward for promoting cooperation. Sci. Rep. 5, 17752 (2015)

    Google Scholar 

  91. Hauert, C., Traulsen, A., Brandt, H., Nowak, M.A., Sigmund, K.: Via freedom to coercion: the emergence of costly punishment. Sci. 316, 1905–1907 (2007)

    MathSciNet  MATH  Google Scholar 

  92. Hilbe, C., Traulsen, A.: Emergence of responsible sanctions without second order free riders, antisocial punishment or spite. Sci. Rep. 2, 458 (2012)

    Google Scholar 

  93. Okada, I., Yamamoto, H., Toriumi, F., Sasaki, T.: The effect of incentives and meta-incentives on the evolution of cooperation. PLoS Comput. Biol. 11, e1004232 (2015). https://doi.org/10.1371/journal.pcbi.1004232

    Google Scholar 

  94. Szolnoki, A., Perc, M.: Antisocial pool rewarding does not deter public cooperation. Proc. R. Soc. B. 282 (2015). https://doi.org/10.1098/rspb.2015.1975

    Google Scholar 

  95. Traulsen, A., Hauert, C., De Silva, H., Nowak, M.A., Sigmund, K.: Exploration dynamics in evolutionary games. Proc. Natl Acad. Sci. USA 106, 709–712 (2009)

    MATH  Google Scholar 

  96. Andreoni, J., Harbaugh, W.T., Vesterlund, L.: The carrot or the stick: rewards, punishments and cooperation. Am. Econ. Rev. 93, 893–902 (2003)

    Google Scholar 

  97. Cinyabuguma, M., Page, T., Putterman, L.: Can second-order punishment deter perverse punishment. Exp. Econ. 9, 265–279 (2006)

    Google Scholar 

  98. Denant-Boemont, L., Masclet, D., Noussair, C.: Punishment, counterpunishment and sanction enforcement in a social dilemma experiment. Econ. Theory 33, 145–167 (2007)

    MathSciNet  MATH  Google Scholar 

  99. Dreber, A., Rand, D.G., Fudenberg, D., Nowak, M.A.: Winners don’t punish. Nature 452, 348–351 (2008)

    Google Scholar 

  100. Egas, M., Riedl, A.: The economics of altruistic punishment and the maintenance of cooperation. Proc. R. Soc. B 275, 871–878 (2008)

    Google Scholar 

  101. Fehr, E., Fischbacher, U.: The nature of human altruism. Nature 425, 785–791 (2003)

    Google Scholar 

  102. Fehr, E., Gachter, S.: Cooperation and punishment in public goods experiments. Am. Econ. Rev. 90, 980–994 (2000)

    Google Scholar 

  103. Fehr, E., Rockenbach, B.: Detrimental effects of sanctions on human altruism. Nature 422, 137–140 (2003)

    Google Scholar 

  104. Gächter, S., Renner, E., Sefton, M.: The long-run benefits of punishment. Science 322, 1510–1510 (2008)

    Google Scholar 

  105. Gurerk, O., Irlenbusch, B., Rockenbach, B.: The competitive advantage of sanctioning institutions. Sci. 312, 108–111 (2006)

    Google Scholar 

  106. Herrmann, B., Thoni, C., Gächter, S.: Antisocial punishment across societies. Science 319, 1362–1367 (2008)

    Google Scholar 

  107. Nikiforakis, N.: Punishment and counter punishment in public good games: can we really govern ourselves? J. Public. Econ. 92, 91–112 (2008)

    Google Scholar 

  108. Rand, D.G., Dreber, A., Ellingsen, T., Fudenberg, D., Nowak, M.A.: Positive interactions promote public cooperation. Science 325, 1272–1275 (2009)

    MathSciNet  MATH  Google Scholar 

  109. Rand, D.G., Nowak, M.A.: The evolution of antisocial punishment in optional public goods games. Nat. Commun. 2, 434 (2011)

    Google Scholar 

  110. Sefton, M., Schupp, R., Walker, M.: The effect of rewards and sanctions in provision of public goods. Econ. Inq. 45, 671–690 (2007)

    Google Scholar 

  111. Walker, J.M., Halloran, M.: Rewards and sanctions and the provision of public goods in one-shot settings. Exp. Econ. 7, 235–247 (2004)

    MATH  Google Scholar 

  112. Wu, J.J., Zhang, B., Zhou, Z.X., He, Q.Q., Zheng, X.D., Cressman, R., Tao, Y.: Costly punishment does not always increase cooperation. Proc. Natl Acad. Sci. USA 106, 17448–17451 (2009)

    Google Scholar 

  113. Sutter, M., Haigner, S., Kocher, M.G.: Choosing the carrot or the stick? Endogenous institutional choice in social dilemma situations. Rev. Econ. Stud. 77, 1540–1566 (2010)

    MathSciNet  MATH  Google Scholar 

  114. Chen, X., Sasaki, T., Brännström, A., Dieckmann, U.: First carrot, then stick: how the adaptive hybridization of incentives promotes cooperation. J. R. Soc. Interface 12 (2015). https://doi.org/10.1098/rsif.2014.0935

    Google Scholar 

  115. Cressman, R., Song, J.W., Zhang, B., Tao, Y.: Cooperation and evolutionary dynamics in the public goods game with institutional incentives. J. Theor. Biol. 299, 144–151 (2012)

    MathSciNet  MATH  Google Scholar 

  116. Oya, G., Ohstuki, H.: Stable polymorphism of cooperators and punishers in a public goods game. J. Theor. Biol. 419, 243–253 (2017)

    MATH  Google Scholar 

  117. Perc, M.: Sustainable institutionalized punishment requires elimination of second-order free-riders. Sci. Rep. 2, 344 (2012)

    Google Scholar 

  118. Sasaki, T., Brännström, A., Dieckmann, U., Sigmund, K.: The take-it-or-leave-it option allows small penalties to overcome social dilemmas. Proc. Natl Acad. Sci. USA 109, 1165–1169 (2012)

    MATH  Google Scholar 

  119. Sasaki, T., Uchida, S., Chen, X.: Voluntary rewards mediate the evolution of pool punishment for maintaining public goods in large populations. Sci. Rep. 5, 8917 (2015)

    Google Scholar 

  120. Schoenmakers, S., Hilbe, C., Blasius, B., Traulsen, A.: Sanctions as honest signals—the evolution of pool punishment by public sanctioning institutions. J. Theor. Biol. 356, 36–46 (2014)

    MathSciNet  MATH  Google Scholar 

  121. Sigmund, K., De-Silva, H., Traulsen, A., Hauert, C.: Social learning promotes institutions for governing the commons. Nature 466, 861–863 (2010)

    Google Scholar 

  122. Szolnoki, A., Perc, M.: Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment. Phys. Rev. X. 7, 041027 (2017). https://doi.org/10.1103/PhysRevX.7.041027

    Google Scholar 

  123. Dong, Y., Sasaki, T., Zhang, B.: The competitive advantage of institutional reward. Proc. R. Soc. B 286, 20190001 (2019). https://doi.org/10.1098/rspb.2019.0001

    Google Scholar 

  124. Zhang, B., An, X., Dong, Y.: Conditional cooperator enhances institutional punishment in public goods game. Appl. Math. Comput. 390, 125600 (2020). https://doi.org/10.1016/j.amc.2020.125600

    MathSciNet  MATH  Google Scholar 

  125. Cressman, R., Wu, J.J., Li, C., Tao, Y.: Game experiments on cooperation through reward and punishment. Biol. Theory 8, 158–166 (2013)

    Google Scholar 

  126. Putterman, L., Tyran, J.L., Kamei, K.: Public goods and voting on formal sanction schemes. J. Public Econ. 95, 1213–1222 (2011)

    Google Scholar 

  127. Traulsen, A., Röhl, T., Milinski, M.: An economic experiment reveals that humans prefer pool punishment to maintain the commons. Proc. R. Soc. B 279, 3716–3721 (2012)

    Google Scholar 

  128. Yamagishi, T.: The provision of a sanctioning system as a public good. J. Pers. Soc. Psychol. 51, 110–116 (1986)

    Google Scholar 

  129. Zhang, B., Li, C., De Silva, H., Bednarik, P., Sigmund, K.: The evolution of sanctioning institutions: an experimental approach to the social contract. Exp. Econ. 17, 285–303 (2014)

    Google Scholar 

  130. Yang, C.L., Zhang, B., Charness, G., Li, C., Lien, J.: Endogenous rewards promote cooperation. Proc. Natl. Acad. Sci. USA 115, 9968–9973 (2018)

    Google Scholar 

  131. Andreoni, J., Gee, L.L.: Gun for hire: delegated enforcement and peer punishment in public goods provision. J. Public Econ. 96, 1036–1046 (2012)

    Google Scholar 

  132. Dong, Y., Zhang, B., Tao, Y.: The dynamics of human behavior in the public goods game with institutional incentives. Sci. Rep. 6(1), 1–7 (2016)

    Google Scholar 

  133. Kamijo, Y., Nihonsugi, T., Takeuchi, A., Funaki, Y.: Sustaining cooperation in social dilemmas: comparison of centralized punishment institutions. Games Econ. Behav. 84, 180–195 (2014)

    MathSciNet  MATH  Google Scholar 

  134. Qin, X., Wang, S.: Using an exogenous mechanism to examine efficient probabilistic punishment. J. Econ. Psychol. 39, 1–10 (2013)

    Google Scholar 

  135. Falkinger, J., Fehr, E., Gächter, S., Winter-Ember, R.: A simple mechanism for the efficient provision of public goods: experimental evidence. Am. Econ. Rev. 90(1), 247–264 (2000)

    Google Scholar 

  136. Huang, S., Dong, Y., Zhang, B.: The optimal incentive in promoting cooperation: punish the worst and do not only reward the best.  Singap. Econ. Rev. (2020). https://doi.org/10.1142/S0217590820500071

    Article  Google Scholar 

  137. Hilbe, C., Nowak, M.A., Traulsen, A.: Adaptive dynamics of extortion and compliance. PLoS ONE 8, e77886 (2013). https://doi.org/10.1371/journal.pone.0077886

    Article  Google Scholar 

  138. Izquierdo, S.S., Izquierdo, L.R., Vega-Redondo, F.: Leave and let leave: a sufcient condition to explain the evolutionary emergence of cooperation. J. Econ. Dyn. Control 46, 91–113 (2014)

    MATH  Google Scholar 

  139. Zhang, B., Li, C., Tao, Y.: Evolutionary stability and the evolution of cooperation in heterogeneous graphs. Dyn. Games Appl. 6, 567–579 (2016)

    MathSciNet  MATH  Google Scholar 

  140. Galbiati, R., Vertova, P.: Obligations and cooperative behaviour in public good games. Games Econ. Behav. 64(1), 146–170 (2008)

    MATH  Google Scholar 

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  1. Laboratory of Mathematics and Complex Systems, Ministry of Education; School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Bo-Yu Zhang & Shan Pei

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  1. Bo-Yu Zhang
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  2. Shan Pei
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Correspondence to Bo-Yu Zhang.

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This work was supported by the National Natural Science Foundation of China (Nos. 71771026 and 71922004).

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Zhang, BY., Pei, S. Game Theory and the Evolution of Cooperation. J. Oper. Res. Soc. China 10, 379–399 (2022). https://doi.org/10.1007/s40305-021-00350-z

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  • DOI: https://doi.org/10.1007/s40305-021-00350-z

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