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Evolutionary Dynamics of Cooperation under the Distributed Prisoner’s Dilemma

  • Flávio L. Pinheiro
  • Francisco C. Santos
  • Jorge M. Pacheco
Conference paper
  • 983 Downloads
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 87)

Abstract

Humans contribute to a broad range of cooperative endeavors. In many of them, the amount or effort contributed often depends on the social context of each individual. Recent evidence has shown how modern societies are grounded in complex and heterogeneous networks of exchange and cooperation, in which some individuals play radically different roles and/or interact more than others. We show that such social heterogeneity drastically affects the behavioral dynamics and promotes cooperative behavior, whenever the social dilemma perceived by each individual is contingent on her/his social context. The multiplicity of roles and contributions induced by realistic population structures is shown to transform an initial defection dominance dilemma into a coordination challenge or even a cooperator dominance game. While locally defection may seem inescapable, globally there is an emergent new dilemma in which cooperation often prevails, illustrating how collective cooperative action may emerge from myopic individual selfishness.

Keywords

Cooperation Complex Networks Self-Organization Evolutionary Game Theory 

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References

  1. 1.
    Milinski, M., Semmann, D., Krambeck, H.J., Marotzke, J.: Stabilizing the earth’s climate is not a losing game: Supporting evidence from public goods experiments. Proc. Natl. Acad. Sci. U S A 103, 3994–3998 (2006)CrossRefGoogle Scholar
  2. 2.
    Dreber, A., Nowak, M.: Gambling for global goods. Proc. Natl. Acad. Sci. U S A 105, 2261–2262 (2008)CrossRefGoogle Scholar
  3. 3.
    Hardin, G.: The tragedy of the commons. Science 162, 1243–1248 (1968)CrossRefGoogle Scholar
  4. 4.
    Nowak, M.A., Sigmund, K.: Evolution of indirect reciprocity by image scoring. Nature 393, 573–577 (1998)CrossRefGoogle Scholar
  5. 5.
    Ohtsuki, H., Iwasa, Y.: How should we define goodness? reputation dynamics in indirect reciprocity. J. Theor. Biol. 231, 107–120 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Nowak, M.A., Sigmund, K.: Evolution of indirect reciprocity. Nature 437, 1291–1298 (2005)CrossRefGoogle Scholar
  7. 7.
    Pacheco, J.M., Santos, F.C., Chalub, F.A.: Stern-judging: A simple, successful norm which promotes cooperation under indirect reciprocity. PLoS Comput. Biol. 2, e178 (2006)Google Scholar
  8. 8.
    Hauert, C., Traulsen, A., Brandt, H., Nowak, M.A., Sigmund, K.: Via freedom fo coercion: The emergence of costly punishment. Science 316, 1905–1907 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Rapoport, A., Chammah, A.M.: Prisoner’s Dilemma: A Study in Conflict and Cooperation. University of Michigan Press (1965)Google Scholar
  10. 10.
    Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press (1998)Google Scholar
  11. 11.
    Nowak, M.A.: Evolutionary dynamics: exploring the equations of life. Belknap/Harvard University Press (2006)Google Scholar
  12. 12.
    Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)CrossRefGoogle Scholar
  13. 13.
    Darwin, C.: The Descent of Man and Selection in Relation to Sex. Murray (1871)Google Scholar
  14. 14.
    Traulsen, A., Nowak, M.: Evolution of cooperation by multilevel selection. Proc. Natl. Acad. Sci. U S A 103, 10952–10955 (2006)CrossRefGoogle Scholar
  15. 15.
    Nowak, M.A., Sasaki, A., Taylor, C., Fudenberg, D.: Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)CrossRefGoogle Scholar
  16. 16.
    Santos, F.C., Pacheco, J.M.: Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95(098104) (2005)Google Scholar
  17. 17.
    Santos, F.C., Pacheco, J.M., Lenaerts, T.: Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl. Acad. Sci. U S A 103, 3490–3494 (2006)CrossRefGoogle Scholar
  18. 18.
    Santos, F.C., Pacheco, J.M.: A new route to the evolution of cooperation. J. Evolution Biol. 19, 726–733 (2006)CrossRefGoogle Scholar
  19. 19.
    Santos, F.C., Rodrigues, J.F., Pacheco, J.M.: Graph topology plays a determinant role in the evolution of cooperation. Proc. Biol. Sci. 273(51-55) (2006)Google Scholar
  20. 20.
    Poncela, J., Gómes-Gardeñes, J., Floría, L.M., Moreno, Y.: Robustness of cooperation in the evolutionary prisoner’s dilemma on complex networks. New J. Phys. 9(187) (2007)Google Scholar
  21. 21.
    Santos, F.C., Santos, M.D., Pacheco, J.: Social diversity promotes the emergence of cooperation in public goods games. Nature 454, 213–216 (2008)CrossRefGoogle Scholar
  22. 22.
    Szabó, G., Fáth, G.: Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ebel, H., Bornholdt, S.: Coevolutionary games on networks. Phys. Rev. E 66(056118) (2002)Google Scholar
  24. 24.
    Zimmermann, M.G., Eguiluz, V.M., San Miguel, M.: Coevolution of dynamical states and interactions in dynamic networks. Phys. Rev. E 69(065102) (2004)Google Scholar
  25. 25.
    Santos, F.C., Pacheco, J.M., Lenaerts, T.: Cooperation prevails when individuals adjust their social ties. PLoS Comput. Biol. 2, e140 (2006)CrossRefGoogle Scholar
  26. 26.
    Pacheco, J.M., Traulsen, A., Nowak, M.A.: Coevolution of strategy and structure in complex networks with dynamical linking. Phys. Rev. Lett. 97, 258103 (2006)CrossRefGoogle Scholar
  27. 27.
    Hanaki, N., Peterhansl, A., Dodds, P.S., Watts, D.J.: Cooperation in evolving social networks. Management Sci. 53, 1036–1050 (2007)CrossRefzbMATHGoogle Scholar
  28. 28.
    Tanimoto, J.: Dilemma solving by the coevolution of networks and strategy in a 2x2 game. Phys. Rev. E 76, 021126 (2007)CrossRefGoogle Scholar
  29. 29.
    Poncela, J., Gómez-Gardeñes, J., Floría, L.M., Sánchez, A., Moreno, Y.: Complex cooperative networks from evolutionary preferential attachment. PLoS One 3, e2449 (2008)CrossRefGoogle Scholar
  30. 30.
    Skyrms, B., Pemantle, R.: A dynamic model of social network formation. Proc. Natl. Acad. Sci. U S A 97, 9340–9346 (2000)CrossRefzbMATHGoogle Scholar
  31. 31.
    Pacheco, J.M., Traulsen, A., Ohtsuki, H., Nowak, M.A.: Repeated games and direct reciprocity under active linking. J. Theor. Biol. 250, 723–731 (2008)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Masuda, N.: Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation. Proc. R Soc. B 274(1620), 1815–1821 (2007)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Tanimoto, J., Yamauchi, A.: Does “game participation cost” affect the advantage of heterogeneous networks for evolving cooperation? Physica A 389(11), 2284–2289 (2010)CrossRefGoogle Scholar
  34. 34.
    Perc, M., Szolnoki, A.: Social diversity and promotion of cooperation in the spatial prisoner’s dilemma game. Phys. Rev. E 77(011904) (2008)Google Scholar
  35. 35.
    Albert, R., Barabási, A.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–98 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Dorogotsev, S.N., Mendes, J.F.F.: Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford University Press (2003)Google Scholar
  37. 37.
    Onnela, J.P., Saramaki, J., Hyvonen, J., Szabó, G., Lazer, D.: Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. U S A 104, 7332–7336 (2007)CrossRefGoogle Scholar
  38. 38.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Amaral, L.A., Scala, A., Barthelemy, M., Stanley, H.: Classes of small-world networks. Proc. Natl. Acad. Sci. U S A 97, 11149–11152 (2000)CrossRefGoogle Scholar
  40. 40.
    Szabó, G., Töke, C.: Evolutionary prisoner’s dilemma game on a square lattice. Phys. Rev. E 58(69–73) (1998)Google Scholar
  41. 41.
    Hauert, C., Szabó, G.: Game theory and physics. Am. J. Phys. 73, 405–414 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Traulsen, A., Nowak, M.A., Pacheco, J.: Stochastic dynamics of invasion and fixation. Phys. Rev. E 74(011909) (2006)Google Scholar
  43. 43.
    Ohtsuki, H., Nowak, M.A.: The replicator equation on graphs. J. Theor. Biol. 243(86-97) (2006)Google Scholar
  44. 44.
    Pacheco, J.M., Pinheiro, F.L., Santos, F.C.: Population structure induces a symmetry breaking favoring the emergence of cooperation. PLoS Comput. Biol. 5(12) (2009)Google Scholar
  45. 45.
    Skyrms, B.: The Stag hunt and the evolution of social structure. Cambridge University Press (2004)Google Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2012

Authors and Affiliations

  • Flávio L. Pinheiro
    • 1
    • 2
  • Francisco C. Santos
    • 3
    • 1
  • Jorge M. Pacheco
    • 4
    • 1
  1. 1.ATP-group, CMAFLisboaPortugal
  2. 2.Centro de Física da Universidade do MinhoBragaPortugal
  3. 3.DEI & INESC-ID, Instituto Superior TécnicoTU LisbonLisboaPortugal
  4. 4.Dep. de Matemática e AplicaçõesUniversidade do MinhoBragaPortugal

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