Promotion of cooperation on networks? The myopic best response case

Topical issue on The Physics Approach to Risk: Agent-Based Models and Networks

Abstract

We study the effect of a network of contacts on the emergence of cooperation on social dilemmas under myopic best response dynamics. We begin by summarizing the main features observed under less intellectually demanding dynamics, pointing out their most relevant general characteristics. Subsequently we focus on the new framework of best response. By means of an extensive numerical simulation program we show that, contrary to the rest of dynamics considered so far, best response is largely unaffected by the underlying network, which implies that, in most cases, no promotion of cooperation is found with this dynamics. We do find, however, nontrivial results differing from the well-mixed population in the case of coordination games on lattices, which we explain in terms of the formation of spatial clusters and the conditions for their advancement, subsequently discussing their relevance to other networks.

PACS

89.65.-s Social and economic systems 87.23.Ge Dynamics of social systems 02.50.Le Decision theory and game theory 89.75.Fb Structures and organization in complex systems 

References

  1. 1.
    E. Pennisi, Science 309, 93 (2005)CrossRefGoogle Scholar
  2. 2.
    W.D. Hamilton, J. Theor. Biol. 7, 1 (1964)CrossRefGoogle Scholar
  3. 3.
    R. Axelrod, W.D. Hamilton, Science 211, 1390 (1981)CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    S.J. Maynard, Evolution and the Theory of Games (Cambridge University Press, Cambridge, 1982)MATHGoogle Scholar
  5. 5.
    M.A. Nowak, Science 314, 1560 (2006)CrossRefADSGoogle Scholar
  6. 6.
    C.P. Roca, J.A. Cuesta, A. Sánchez, Phys. Rev. Lett. 97, 158701 (2006)CrossRefADSGoogle Scholar
  7. 7.
    M.A. Nowak, R.M. May, Nature 359, 826 (1992)CrossRefADSGoogle Scholar
  8. 8.
    A. Rapoport, A.M. Chammah, Prisoner’s Dilemma: A Study in Conflict and Cooperation (University of Michigan Press, Ann Arbor, 1965)Google Scholar
  9. 9.
    G. Szabó, G. Fáth, Phys. Rep. 446, 97 (2007)CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    C.P. Roca, J.A. Cuesta, A. Sánchez, e-print arXiv:0806.1649 (2008)Google Scholar
  11. 11.
    F.C. Santos, J.M. Pacheco, T. Lenaerts, Proc. Natl. Acad. Sci. USA 103, 3490 (2006)CrossRefADSGoogle Scholar
  12. 12.
    J. Gómez-Gardeñes, M. Campillo, L.M. Floría, Y. Moreno, Phys. Rev. Lett. 98, 108103 (2007)CrossRefADSGoogle Scholar
  13. 13.
    A. Matsui, J. Econ. Theory 57, 343 (1992)MATHGoogle Scholar
  14. 14.
    L. Blume, Games Econ. Behav. 5, 387 (1993)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    G. Ellison, Econometrica 61, 1047 (1993)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998)MATHGoogle Scholar
  17. 17.
    M.W. Macy, A. Flache, Proc. Natl. Acad. Sci. USA 99, 7229 (2002)CrossRefADSGoogle Scholar
  18. 18.
    A.N. Licht, Yale J. Int. Law 24, 61 (1999)Google Scholar
  19. 19.
    B. Skyrms, The Stag Hunt and the Evolution of Social Structure (Cambridge University Press, Cambridge, 2003)Google Scholar
  20. 20.
    J.S. Maynard, G.R. Price, Nature 246, 15 (1973)CrossRefGoogle Scholar
  21. 21.
    R. Sugden, Economics of Rights, Co-operation and Welfare, 2nd edn. (Palgrave Macmillan, Hampshire, 2004)Google Scholar
  22. 22.
    H. Gintis, Game Theory Evolving (Princeton University Press, 2000)Google Scholar
  23. 23.
    A. Rapoport, M. Guyer, General Systems 11, 203 (1966)Google Scholar
  24. 24.
    M.E.J. Newman, SIAM Review 45, 167 (2003)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    C. Hauert, M. Doebeli, Nature 428, 643 (2004)CrossRefADSGoogle Scholar
  26. 26.
    M. Sysi-Aho, J. Saramäki, J. Kertész, K. Kaski, Eur. Phys. J. B 44, 129 (2005)CrossRefADSGoogle Scholar
  27. 27.
    B. Bollobas, Random Graphs (Cambridge University Press, Cambridge, 2001)MATHGoogle Scholar
  28. 28.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999)CrossRefMathSciNetGoogle Scholar
  29. 29.
    K. Klemm, V.M. Eguíluz, Phys. Rev. E 65, 036123 (2002)CrossRefADSGoogle Scholar
  30. 30.
    M.O. Jackson, A. Wolinsky, J. Econ. Theory 71, 44 (1996)MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    S. Goyal, F. Vega-Redondo, J. Econ. Theory 137, 460 (2007)MATHCrossRefGoogle Scholar
  32. 32.
    C. Taylor, D. Fudenberg, A. Sasaki, M.A. Nowak, Bull. Math. Biol. 66, 1621 (2004)CrossRefMathSciNetGoogle Scholar
  33. 33.
    V. Hatzopoulos, H.J. Jensen, Phys. Rev. E 78, 011904 (2008)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de MatemáticasUniversidad Carlos III de MadridMadridSpain
  2. 2.Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCMMadridSpain
  3. 3.Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de ZaragozaZaragozaSpain

Personalised recommendations