Skip to main content
SpringerLink
Log in

Promotion of cooperation on networks? The myopic best response case

  • Topical issue on The Physics Approach to Risk: Agent-Based Models and Networks
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Pennisi, Science 309, 93 (2005)

    Article  Google Scholar 

  2. W.D. Hamilton, J. Theor. Biol. 7, 1 (1964)

    Article  Google Scholar 

  3. R. Axelrod, W.D. Hamilton, Science 211, 1390 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  4. S.J. Maynard, Evolution and the Theory of Games (Cambridge University Press, Cambridge, 1982)

    MATH  Google Scholar 

  5. M.A. Nowak, Science 314, 1560 (2006)

    Article  ADS  Google Scholar 

  6. C.P. Roca, J.A. Cuesta, A. Sánchez, Phys. Rev. Lett. 97, 158701 (2006)

    Article  ADS  Google Scholar 

  7. M.A. Nowak, R.M. May, Nature 359, 826 (1992)

    Article  ADS  Google Scholar 

  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. G. Szabó, G. Fáth, Phys. Rep. 446, 97 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  10. C.P. Roca, J.A. Cuesta, A. Sánchez, e-print arXiv:0806.1649 (2008)

  11. F.C. Santos, J.M. Pacheco, T. Lenaerts, Proc. Natl. Acad. Sci. USA 103, 3490 (2006)

    Article  ADS  Google Scholar 

  12. J. Gómez-Gardeñes, M. Campillo, L.M. Floría, Y. Moreno, Phys. Rev. Lett. 98, 108103 (2007)

    Article  ADS  Google Scholar 

  13. A. Matsui, J. Econ. Theory 57, 343 (1992)

    MATH  Google Scholar 

  14. L. Blume, Games Econ. Behav. 5, 387 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Ellison, Econometrica 61, 1047 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998)

    MATH  Google Scholar 

  17. M.W. Macy, A. Flache, Proc. Natl. Acad. Sci. USA 99, 7229 (2002)

    Article  ADS  Google Scholar 

  18. A.N. Licht, Yale J. Int. Law 24, 61 (1999)

    Google Scholar 

  19. B. Skyrms, The Stag Hunt and the Evolution of Social Structure (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  20. J.S. Maynard, G.R. Price, Nature 246, 15 (1973)

    Article  Google Scholar 

  21. R. Sugden, Economics of Rights, Co-operation and Welfare, 2nd edn. (Palgrave Macmillan, Hampshire, 2004)

    Google Scholar 

  22. H. Gintis, Game Theory Evolving (Princeton University Press, 2000)

  23. A. Rapoport, M. Guyer, General Systems 11, 203 (1966)

    Google Scholar 

  24. M.E.J. Newman, SIAM Review 45, 167 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  25. C. Hauert, M. Doebeli, Nature 428, 643 (2004)

    Article  ADS  Google Scholar 

  26. M. Sysi-Aho, J. Saramäki, J. Kertész, K. Kaski, Eur. Phys. J. B 44, 129 (2005)

    Article  ADS  Google Scholar 

  27. B. Bollobas, Random Graphs (Cambridge University Press, Cambridge, 2001)

    MATH  Google Scholar 

  28. A.-L. Barabási, R. Albert, Science 286, 509 (1999)

    Article  MathSciNet  Google Scholar 

  29. K. Klemm, V.M. Eguíluz, Phys. Rev. E 65, 036123 (2002)

    Article  ADS  Google Scholar 

  30. M.O. Jackson, A. Wolinsky, J. Econ. Theory 71, 44 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  31. S. Goyal, F. Vega-Redondo, J. Econ. Theory 137, 460 (2007)

    Article  MATH  Google Scholar 

  32. C. Taylor, D. Fudenberg, A. Sasaki, M.A. Nowak, Bull. Math. Biol. 66, 1621 (2004)

    Article  MathSciNet  Google Scholar 

  33. V. Hatzopoulos, H.J. Jensen, Phys. Rev. E 78, 011904 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain

    C. P. Roca, J. A. Cuesta & A. Sánchez

  2. Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, 28006, Madrid, Spain

    A. Sánchez

  3. Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, 50009, Zaragoza, Spain

    A. Sánchez

Authors
  1. C. P. Roca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. A. Cuesta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Sánchez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Sánchez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roca, C., Cuesta, J. & Sánchez, A. Promotion of cooperation on networks? The myopic best response case. Eur. Phys. J. B 71, 587–595 (2009). https://doi.org/10.1140/epjb/e2009-00189-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2009-00189-0

PACS

Search

Navigation