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Correlation of Positive and Negative Reciprocity Fails to Confer an Evolutionary Advantage: Phase Transitions to Elementary Strategies

Attila Szolnoki1 and Matjaž Perc2

  • 1Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
  • 2Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia

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Phys. Rev. X 3, 041021 – Published 27 November, 2013

DOI: https://doi.org/10.1103/PhysRevX.3.041021

Abstract

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.

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Popular Summary

One of the fundamental traits that set us apart from other animal species is our remarkable ability for cooperation with biologically unrelated other individuals. To explain the emergence and prevalence of this human trait has been one of the big challenges for social science. One of the theories is the so-called strong reciprocity hypothesis: If someone is kind to us, we tend to be kind in return. Similarly, if someone is unfair or exploitative, we tend to retaliate without much sympathy or stop cooperating. And, these two tendencies, or positive and negative reciprocity, are thought to be correlated to give us optimal evolutionary predispositions for cooperation. Recent human experiments, however, appear to reject this hypothesis, and our everyday experiences leave us with the impression that most people tend to either reward success or punish unfairness, but seldom do both. Which should we then believe or doubt, the hypothesis, or the conclusion of the human experiments? In this paper, we lend significant support to the latter with statistical physical simulations of evolutionary game models involving different reciprocity scenarios.

Our models are based on the so-called public goods games that involve both cooperators and defectors. Cooperators consist of three distinct groups, those that practice only the positive or negative reciprocity strategy and those that practice both, and all contribute to “the public goods,” while defectors contribute nothing. Defectors and cooperators are homogeneously distributed among the total population, and the former receive reward from an even distribution of the overall public goods, but also punishment (or a “fine”) from their cooperator neighbors that practice negative reciprocity. Both cooperators and defectors may change their strategy based on the payoffs they receive.

The question we focus on is whether practicing both positive and negative reciprocity strategies simultaneously confers an evolutionary advantage to individuals adopting such a correlated strategy. Through Monte Carlo simulations of the game playing, our model at once predicts both the emergence of a range of social behaviors, including indirect territorial competition and spontaneous emergence of cyclic dominance, and the very limited presence of the correlated strategy in very narrow and rather unrealistic parameter regions. Either only rewarding or only punishing is far superior and more effective in deterring defection.

We hope that our work will inspire more interdisciplinary theoretical and experimental work aimed at advancing our understanding of the evolution of human cooperation. The richness of our model in terms of exhibiting fundamentally different “social behaviors” (or nonequilibrium phenomena) should also make it an interesting playground for those physicists whose focus is on fundamental nonequilibrium physics.

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References (67)

  1. M. A. Nowak and R. Highfield, SuperCooperators: Altruism, Evolution, and Why We Need Each Other to Succeed (Free Press, New York, 2011).
  2. C. L. Apicella, F. W. Marlowe, J. H. Fowler, and N. A. Christakis, Social Networks and Cooperation in Hunter-Gatherers, Nature (London) 481, 497 (2012).
  3. E. Fehr and K. M. Schmidt, A Theory of Fairness, Competition, and Cooperation, Q. J. Econ. 114, 817 (1999).
  4. J. Henrich, R. Boyd, S. Bowles, C. Camerer, E. Fehr, H. Gintis, and R. McElreath, In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies, Am. Econ. Rev. 91, 73 (2001).
  5. E. Fehr and S. Gachter, Cooperation and Punishment in Public Goods Experiments, Am. Econ. Rev. 90, 980 (2000).
  6. J. Henrich, R. McElreath, A. Barr, J. Ensminger, C. Barrett, A. Bolyanatz, J. C. Cardenas, M. Gurven, E. Gwako, N. Henrich, C. Lesorogol, F. Marlowe, D. Tracer, and J. Ziker, Costly Punishment across Human Societies, Science 312, 1767 (2006).
  7. K. Sigmund, Punish or Perish? Retaliation and Collaboration among Humans, Trends Ecol. Evol. 22, 593 (2007).
  8. J. M. Burkart, E. Fehr, C. Efferson, and C. P. van Schaik, Other-Regarding Preferences in a Non-human Primate: Common Marmosets Provision Food Altruistically, Proc. Natl. Acad. Sci. U.S.A. 104, 19762 (2007).
  9. D. Proctor, R. A. Williamson, F. B. M. de Waal, and S. F. Brosnan, Chimpanzees Play the Ultimatum Game, Proc. Natl. Acad. Sci. U.S.A. 110, 2070 (2013).
  10. S. Bowles and H. Gintis, A Cooperative Species: Human Reciprocity and Its Evolution (Princeton University Press, Princeton, NJ, 2011).
  11. S. B. Hrdy, Mothers and Others: The Evolutionary Origins of Mutual Understanding (Harvard University Press, Cambridge, MA, 2011).
  12. G. Szabó and G. Fáth, Evolutionary Games on Graphs, Phys. Rep. 446, 97 (2007).
  13. M. Perc and A. Szolnoki, Coevolutionary Games—A Mini Review, BioSystems 99, 109 (2010).
  14. M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L. M. Floría and Y. Moreno, Evolutionary Dynamics of Group Interactions on Structured Populations: A Review, J. R. Soc. Interface 10, 20120997 (2013).
  15. M. A. Nowak, Evolving Cooperation, J. Theor. Biol. 299, 1 (2012).
  16. D. G. Rand and M. A. Nowak, Human Cooperation, Trends Cogn. Sci. 17, 413 (2013).
  17. M. A. Nowak, Five Rules for the Evolution of Cooperation, Science 314, 1560 (2006).
  18. M. A. Nowak and R. M. May, Evolutionary Games and Spatial Chaos, Nature (London) 359, 826 (1992).
  19. C. Hauert and M. Doebeli, Spatial Structure Often Inhibits the Evolution of Cooperation in the Snowdrift Game, Nature (London) 428, 643 (2004).
  20. F. C. Santos and J. M. Pacheco, Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation, Phys. Rev. Lett. 95, 098104 (2005).
  21. F. Fu, D. I. Rosenbloom, L. Wang, and M. A. Nowak, Imitation Dynamics of Vaccination Behaviour on Social Networks, Proc. R. Soc. B 278, 42 (2011).
  22. C. Gracia-Lázaro, A. Ferrer, G. Ruiz, A. Tarancón, J. A. Cuesta, A. Sánchez, and Y. Moreno, Heterogeneous Networks Do Not Promote Cooperation When Humans Play a Prisoner’s Dilemma, Proc. Natl. Acad. Sci. U.S.A. 109, 12922 (2012).
  23. H. Gintis, Strong Reciprocity and Human Sociality, J. Theor. Biol. 206, 169 (2000).
  24. E. Fehr, U. Fischbacher, and S. Gächter, Strong Reciprocity, Human Cooperation and the Enforcement of Social Norms, Human Nature 13, 1 (2002).
  25. R. Boyd, H. Gintis, S. Bowles, and P. J. Richerson, The Evolution of Altruistic Punishment, Proc. Natl. Acad. Sci. U.S.A. 100, 3531 (2003).
  26. S. Bowles and H. Gintis, The Evolution of Strong Reciprocity: Cooperation in Heterogeneous Populations, Theor. Popul. Biol. 65, 17 (2004).
  27. T. Yamagishi, Y. Horita, N. Mifune, H. Hashimoto, Y. Li, M. Shinada, A. Miura, K. Inukai, H. Takagishi, and D. Simunovic, Rejection of Unfair Offers in the Ultimatum Game Is No Evidence of Strong Reciprocity, Proc. Natl. Acad. Sci. U.S.A. 109, 20364 (2012).
  28. B. Egloff, D. Richter, and S. C. Schmukle, Need for Conclusive Evidence That Positive and Negative Reciprocity Are Unrelated, Proc. Natl. Acad. Sci. U.S.A. 110, E786 (2013).
  29. W. Güth, R. Schmittberger, and B. Schwarze, An Experimental Analysis of Ultimatum Bargaining, J. Econ. Behav. Organ. 3, 367 (1982).
  30. D. G. Rand, A. Dreber, T. Ellingsen, D. Fudenberg, and M. A. Nowak, Positive Interactions Promote Public Cooperation, Science 325, 1272 (2009).
  31. D. G. Rand, S. Arbesman, and N. A. Christakis, Dynamic Social Networks Promote Cooperation in Experiments with Humans, Proc. Natl. Acad. Sci. U.S.A. 108, 19193 (2011).
  32. K. Sigmund, E. Fehr, and M. A. Nowak, The Economics of Fair Play, Sci. Am. 286, 82 (2002).
  33. K. Sigmund, Games of Life: Exploration in Ecology, Evolution and Behavior (Oxford University Press, Oxford, England, 1993).
  34. J. W. Weibull, Evolutionary Game Theory (MIT Press, Cambridge, MA, 1995).
  35. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, England, 1998).
  36. M. A. Nowak, Evolutionary Dynamics (Harvard University Press, Cambridge, MA, 2006).
  37. K. Sigmund, The Calculus of Selfishness (Princeton University Press, Princeton, NJ, 2010).
  38. K. Binder and D. K. Hermann, Monte Carlo Simulations in Statistical Physics (Springer, Heidelberg, 1988).
  39. T. M. Liggett, Interacting Particle Systems (Springer, New York, 1985).
  40. C. Hilbe and K. Sigmund, Incentives and Opportunism: From the Carrot to the Stick, Proc. R. Soc. B 277, 2427 (2010).
  41. K. Sigmund, H. De Silva, A. Traulsen, and C. Hauert, Social Learning Promotes Institutions for Governing the Commons, Nature (London) 466, 861 (2010).
  42. D. G. Rand and M. A. Nowak, The Evolution of Antisocial Punishment in Optional Public Goods Games, Nat. Commun. 2, 434 (2011).
  43. C. Hilbe and A. Traulsen, Emergence of Responsible Sanctions without Second Order Free Riders, Antisocial Punishment or Spite, Sci. Rep. 2, 458 (2012).
  44. M. Perc and A. Szolnoki, Self-Organization of Punishment in Structured Populations, New J. Phys. 14, 043013 (2012).
  45. A. Szolnoki and M. Perc, Evolutionary Advantages of Adaptive Rewarding, New J. Phys. 14, 093016 (2012).
  46. H. Brandt, C. Hauert, and K. Sigmund, Punishment and Reputation in Spatial Public Goods Games, Proc. R. Soc. B 270, 1099 (2003).
  47. A. Szolnoki, M. Perc, and G. Szabó, Topology-Independent Impact of Noise on Cooperation in Spatial Public Goods Games, Phys. Rev. E 80, 056109 (2009).
  48. E. Fehr, Don’t Lose Your Reputation, Nature (London) 432, 449 (2004).
  49. J. H. Fowler, Second-Order Free-Riding Problem Solved?, Nature (London) 437, E8 (2005).
  50. M. Nakamaru and Y. Iwasa, Evolution of Altruism by Costly Punishment in Lattice-Structured Population: Score-Dependent Viability versus Score-Dependent Fertility, Evol. Ecol. Res. 7, 853 (2005).
  51. D. Helbing, A. Szolnoki, M. Perc, and G. Szabó, Punish, but Not Too Hard: How Costly Punishment Spreads in the Spatial Public Goods Game, New J. Phys. 12, 083005 (2010).
  52. A. Szolnoki and M. Perc, Group-Size Effects on the Evolution of Cooperation in the Spatial Public Goods Game, Phys. Rev. E 84, 047102 (2011).
  53. A. Szolnoki, G. Szabó, and L. Czakó, Competition of Individual and Institutional Punishments in Spatial Public Goods Games, Phys. Rev. E 84, 046106 (2011).
  54. A. Szolnoki, G. Szabó, and M. Perc, Phase Diagrams for the Spatial Public Goods Game with Pool Punishment, Phys. Rev. E 83, 036101 (2011).
  55. D. Helbing, A. Szolnoki, M. Perc, and G. Szabó, Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions, PLoS Comput. Biol. 6, e1000758 (2010).
  56. A. Szolnoki and M. Perc, Effectiveness of Conditional Punishment for the Evolution of Public Cooperation, J. Theor. Biol. 325, 34 (2013).
  57. T. Reichenbach, M. Mobilia, and E. Frey, Mobility Promotes and Jeopardizes Biodiversity in Rock-Paper-Scissors Games, Nature (London) 448, 1046 (2007).
  58. T. Reichenbach, M. Mobilia, and E. Frey, Noise and Correlations in a Spatial Population Model with Cyclic Competition, Phys. Rev. Lett. 99, 238105 (2007).
  59. M. Mobilia, Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations, J. Theor. Biol. 264, 1 (2010).
  60. M. Mobilia, Fixation and Polarization in a Three-Species Opinion Dynamics Model, Europhys. Lett. 95, 50002 (2011).
  61. Z.-X. Wu, X.-J. Xu, Y. Chen, and Y.-H. Wang, Spatial Prisoner’s Dilemma Game with Volunteering in Newman-Watts Small-World Networks, Phys. Rev. E 71, 037103 (2005).
  62. A. Szolnoki, M. Perc, and G. Szabó, Defense Mechanisms of Empathetic Players in the Spatial Ultimatum Game, Phys. Rev. Lett. 109, 078701 (2012).
  63. C. Gracia-Lázaro, J. A. Cuesta, A. Sánchez, and Y. Moreno, Human Behavior in Prisoner’s Dilemma Experiments Suppresses Network Reciprocity, Sci. Rep. 2, 325 (2012).
  64. D. G. Hernández and D. H. Zanette, Critical Transition Induced by Neighbourhood Size in Evolutionary Spatial Games, Eur. Phys. J. B 82, 361 (2011).
  65. S. Steingrube, M. Timme, F. Wörgötter, and P. Manoonpong, Self-Organized Adaptation of a Simple Neural Circuit Enables Complex Robot Behaviour, Nat. Phys. 6, 224 (2010).
  66. S. Lee, P. Holme, and Z.-X. Wu, Emergent Hierarchical Structures in Multiadaptive Games, Phys. Rev. Lett. 106, 028702 (2011).
  67. F. Fu, C. E. Tarnita, N. A. Christakis, L. Wang, D. G. Rand, and M. A. Nowak, Evolution of In-Group Favoritism, Sci. Rep. 2, 460 (2012).

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Phys. Rev. X 3, 041021– Published 27 November, 2013
  • Received 18 August 2013
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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