Biological Theory

, Volume 3, Issue 2, pp 114–122 | Cite as

Public Goods With Punishment and Abstaining in Finite and Infinite Populations

  • Christoph Hauert
  • Arne Traulsen
  • Hannelore De Silva née Brandt
  • Martin A. Nowak
  • Karl Sigmund


The evolution and maintenance of cooperation in human and animal societies challenge various disciplines ranging from evolutionary biology to anthropology, social sciences, and economics. In social interactions, cooperators increase the welfare of the group at some cost to themselves whereas defectors attempt to free ride and neither provide benefits nor incur costs. The problem of cooperation becomes even more pronounced when increasing the number of interacting individuals. Punishment and voluntary participation have been identified as possible factors to support cooperation and prevent cheating. Typically, punishment behavior is unable to gain a foothold in a population, while volunteering alone can efficiently prevent deadlocks in states of mutual defection but is unable to stabilize cooperation. The combined effects of the two mechanisms have surprisingly different consequences in finite and infinite populations. Here we provide a detailed comparison of the two scenarios and demonstrate that driven by the inherent stochasticity of finite populations, the possibility to abstain from social interactions plays a pivotal role, which paves the way for the establishment of cooperation and punishment.


cooperation evolutionary game theory public goods games punishment social dilemmas voluntary participation 


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  1. Axelrod R (1984) The Evolution of Cooperation. New York: Basic Books.Google Scholar
  2. Axelrod R, Hamilton WD (1981) The evolution of cooperation. Science 211: 1390–1396.CrossRefGoogle Scholar
  3. Boyd R, Gintis H, Bowles S, Richerson P (2003) The evolution of altruistic punishment. Proceedings of the National Academy of Sciences of the USA 100: 3531–3535.CrossRefGoogle Scholar
  4. Boyd R, Mathew S (2007) A narrow road to cooperation. Science 316: 1858–1859.CrossRefGoogle Scholar
  5. Boyd R, Richerson PJ (1988) The evolution of reciprocity in sizeable groups. Journal of Theoretical Biology 132: 337–356.CrossRefGoogle Scholar
  6. Boyd R, Richerson PJ (1992) Punishment allows the evolution of cooperation (or anything else) in sizable groups. Ethnology and Sociobiology 13: 171–195.CrossRefGoogle Scholar
  7. Brandt H, Hauert C, Sigmund K (2003) Cooperation, punishment and reputation in spatial games. Proceedings of Royal Society of London B 270: 1099–1104.CrossRefGoogle Scholar
  8. Brandt H, Hauert C, Sigmund K (2006) Punishing and abstaining for public goods. Proceedings of the National Academy of Sciences of the USA 103(2): 495–497.CrossRefGoogle Scholar
  9. Clutton-Brock TH, Parker GA (1995) Punishment in animal societies. Nature 373: 209–216.CrossRefGoogle Scholar
  10. Colman AM (1995) Game Theory and Its Applications in the Social and Biological Sciences. Oxford: Butterworth-Heinemann.Google Scholar
  11. Crow JF, Kimura M (1970) An Introduction to Population Genetics Theory. New York: Harper and Row.Google Scholar
  12. Dawes RM (1980) Social dilemmas. Annual Review of Psychology 31: 169–193.CrossRefGoogle Scholar
  13. De Silva H (2008) Interactive simulations.
  14. Dugatkin LA (1997) Cooperation Among Animals: An Evolutionary Perspective. Oxford: Oxford University Press.Google Scholar
  15. Fehr E, Fischbacher U (2004) Third-party punishment and social norms. Evolution and Human Behavior 25: 63–87.CrossRefGoogle Scholar
  16. Fehr E, Gächter S (2002) Altruistic punishment in humans. Nature 415: 137–140.CrossRefGoogle Scholar
  17. Fehr E, Rockenbach B (2003) Detrimental effects of sanctions on human altruism. Nature 422: 137–140.CrossRefGoogle Scholar
  18. Fletcher J, Zwick M (2004) Strong altruism can evolve in randomly formed groups. Journal of Theoretical Biology 228: 303–313.CrossRefGoogle Scholar
  19. Fowler JH (2005) Altruistic punishment and the origin of cooperation. Proceedings of the National Academy of Sciences of the USA 102(19): 7047–7049.CrossRefGoogle Scholar
  20. Fudenberg D, Nowak MA, Taylor C, Imhof LA (2006) Evolutionary game dynamics in finite populations with strong selection and weak mutation. Theoretical Population Biology 70: 352–363.CrossRefGoogle Scholar
  21. Grafen A (1985) A geometric view of relatedness. In: Oxford Surveys in Evolutionary Biology, Vol. 2, 28–89. Oxford: Oxford University Press.Google Scholar
  22. Hamilton WD (1964) The genetical evolution of social behaviour I. Journal of Theoretical Biology 7: 1–16.CrossRefGoogle Scholar
  23. Hardin G (1968) The tragedy of the commons. Science 162: 1243–1248.CrossRefGoogle Scholar
  24. Hauert C (2001) Fundamental clusters in spatial 2 × 2 games. Proceedings of Royal Society of London B 268: 761–769.CrossRefGoogle Scholar
  25. Hauert C (2007) Virtuallabs: Interactive tutorials on evolutionary game theory.
  26. Hauert C, De Monte S, Hofbauer J, Sigmund K (2002a) Replicator dynamics in optional public goods games. Journal of Theoretical Biology 218: 187–194.CrossRefGoogle Scholar
  27. Hauert C, De Monte S, Hofbauer J, Sigmund K (2002b) Volunteering as red queen mechanism for cooperation in public goods games. Science 296: 1129–1132.CrossRefGoogle Scholar
  28. Hauert C, Michor F, Nowak M, Doebeli M (2006) Synergy and discounting of cooperation in social dilemmas. Journal of Theoretical Biology 239: 195–202.CrossRefGoogle Scholar
  29. Hauert C, Schuster HG (1997) Effects of increasing the number of players and memory size in the iterated prisoner’s dilemma: A numerical approach. Proceedings of Royal Society of London B 264: 513–519.CrossRefGoogle Scholar
  30. Hauert C, Traulsen A, Brandt H, Nowak MA, Sigmund K (2007) Via freedom to coercion: The emergence of costly punishment. Science 316: 1905–1907.CrossRefGoogle Scholar
  31. Hofbauer J, Sigmund K (1998) Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  32. Imhof LA, Fudenberg D, Nowak MA (2005) Evolutionary cycles of cooperation and defection. Proceedings of the National Academy of Sciences of the USA 102(31): 10797–10800.CrossRefGoogle Scholar
  33. Kagel JH, Roth AE, eds (1995) The Handbook of Experimental Economics. Princeton: Princeton University Press.Google Scholar
  34. Karlin S, Taylor HM (1975) First Course in Stochastic Processes, 2nd ed. London: Academic Press.Google Scholar
  35. Lindgren K (1991) Evolutionary phenomena in simple dynamics. In: Artificial Life II (Langton CG, Farmer JD, Rasmussen S, Taylor C, eds), Vol. X of Proceedings of the Santa Fe Institute Studies in the Sciences of Complexity pp. 295–312. Redwood City, CA: Addison-Wesley.Google Scholar
  36. Maynard Smith J (1964) Group selection and kin selection. Nature 201(4942): 1145–1147.CrossRefGoogle Scholar
  37. Moran PAP (1962) The Statistical Processes of Evolutionary Theory. Oxford, UK: Clarendon.Google Scholar
  38. Nakamaru M, Iwasa Y (2006) The coevolution of altruism and punishment: Role of the selfish punisher. Journal of Theoretical Biology 240(3): 475–488.CrossRefGoogle Scholar
  39. Nowak MA (2006a) Evolutionary Dynamics. Cambridge, MA: Harvard University Press.Google Scholar
  40. Nowak, MA (2006b) Five rules for the evolution of cooperation. Science 314: 1560–1563.CrossRefGoogle Scholar
  41. Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359: 826–829.CrossRefGoogle Scholar
  42. Nowak MA, Sasaki A, Taylor C, Fudenberg D (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature 428: 646–650.CrossRefGoogle Scholar
  43. Nowak MA, 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.CrossRefGoogle Scholar
  44. Nowak MA, Sigmund K (1998) Evolution of indirect reciprocity by image scoring. Nature 393: 573–577.CrossRefGoogle Scholar
  45. Nowak MA, Sigmund K (2004) Evolutionary dynamics of biological games. Science 303: 793–799.CrossRefGoogle Scholar
  46. Nowak MA, Sigmund K (2005) Evolution of indirect reciprocity. Nature 437: 1291–1298.CrossRefGoogle Scholar
  47. Ohtsuki H, Hauert C, Lieberman E, Nowak MA (2006) A simple rule for the evolution of cooperation on graphs and social networks. Nature 441: 502–505.CrossRefGoogle Scholar
  48. Olson M (1965) The Logic of Collective Action. Cambridge, MA: Harvard University Press.Google Scholar
  49. Queller DC (1985) Kinship, reciprocity and synergism in the evolution of social behavior. Nature 318: 366–367.CrossRefGoogle Scholar
  50. Rockenbach B, Milinski M (2006) Indirect reciprocity resolves the efficiency dilemma of costly punishment. Nature 444: 718–723.CrossRefGoogle Scholar
  51. Sigmund K, Hauert C, Nowak MA (2001) Reward and punishment. Proceedings of National Academic Science 98: 10757–10762.CrossRefGoogle Scholar
  52. Taylor C, Fudenberg D, Sasaki A, Nowak MA (2004) Evolutionary game dynamics in finite populations. Bulletin of Mathematical Biology 66: 1621–1644.CrossRefGoogle Scholar
  53. Taylor P, Jonker L (1978) Game dynamics and evolutionarily stable strategies. Mathematical Biosciences 40: 145–156.CrossRefGoogle Scholar
  54. Traulsen A, Claussen JC, Hauert C (2005) Coevolutionary dynamics: From finite to infinite populations. Physical Review Letters 95: 238701.CrossRefGoogle Scholar
  55. Traulsen A, Nowak MA (2006) Evolution of cooperation by multilevel selection. Proceedings of the National Academy of Sciences of the USA 103(29): 10952–10955.CrossRefGoogle Scholar
  56. Traulsen A, Nowak MA, Pacheco JM (2006) Stochastic dynamics of invasion and fixation. Physical Review E 74: 011909.CrossRefGoogle Scholar
  57. Trivers RL (1971) The evolution of reciprocal altruism. Quaterly Review of Biology 46: 35–57.CrossRefGoogle Scholar
  58. Yamagishi T (1986) The provision of a sanctioning system as a public good. Journal of Personality and Social Psychology 51: 110–116.CrossRefGoogle Scholar

Copyright information

© Konrad Lorenz Institute for Evolution and Cognition Research 2008

Authors and Affiliations

  • Christoph Hauert
    • 1
    • 2
  • Arne Traulsen
    • 1
    • 3
  • Hannelore De Silva née Brandt
    • 4
  • Martin A. Nowak
    • 1
  • Karl Sigmund
    • 5
    • 6
  1. 1.Program for Evolutionary Dynamics Department of Organismic and Evolutionary Biology and Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Max-Planck-Institute for Evolutionary BiologyPlönGermany
  4. 4.Department of FinanceVienna University of Economics and Business AdministrationViennaAustria
  5. 5.Faculty of MathematicsUniversity of ViennaViennaAustria
  6. 6.International Institute for Applied Systems AnalysisLaxenburgAustria

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