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Computational Economics

, Volume 46, Issue 1, pp 1–14 | Cite as

Partially and Wholly Overlapping Networks: The Evolutionary Dynamics of Social Dilemmas on Social Networks

  • Yanlong Zhang
Article

Abstract

It has been widely accepted that the evolution of cooperation in social dilemmas is likely to have simultaneous effects on different levels of networks—that is, overlapping networks. In this scenario, we apply the evolutionary dynamics of social dilemmas (the Prisoner’s dilemma and the Stag Hunt) to two levels of networks, playing network interaction game (scale-free networks) and imitating the strategies of dynamic learning networks by concentrating on the levels of dynamically overlapping levels in both networks. It was found that the higher level of dynamically overlap can promote the emergence of cooperation in the Prisoner’s Dilemma and the Stag Hunt. When networks overlap dynamically, it leads to cooperation in the Stag Hunt; when the networks do not overlap, cooperation will not occur in the Prisoner’s dilemma. Specifically, if two kinds of networks in the real world truly dynamically overlap at least partially, in some sense, the self-organizing phenomenon arising out of the overlapping effect could solve “coordination failure” in the market without external enforcement mechanisms, which contradicts conventional intervention polices.

Keywords

Overlapping networks Social dilemmas Evolutioanry dyanmics Self-organizing phenomenon 

Notes

Acknowledgments

I am particularly grateful to Prof. Wolfram Elsner, leading scholar in evolutionary political economics, for his rigorous cultivation of critical thought and active support. I am grateful to the China Scholarship Council for a scholarship, and to Ulrich Witt at the Max Planck Institute of Economics and Alondra Nelson at Columbia University for their knowledge and input during the talk. Finally, I am grateful to the three anonymous referees for their helpful comments.

References

  1. Abramson, G., & Kuperman, M. (2001). Social games in a social network. Physical Review E, 63, 030901.CrossRefGoogle Scholar
  2. Axelrod, R., Riolo, R., & Cohen, M. D. (2002). Beyond geography: Cooperation with persistent links in the absence of clustered neighborhood. Personality and Social Psychology Review, 6(4), 341–346.Google Scholar
  3. Bala, V., & Goyal, S. (2000). A noncooperative model of network formation. Econometrica, 68(5), 1181–1229.Google Scholar
  4. Barabási, A., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.CrossRefGoogle Scholar
  5. Binmore, K. (1994). Playing fair: Game theory and the social contract. Cambridge, USA: MIT Press.Google Scholar
  6. Cassar, A. (2007). Coordination and cooperation in local, random and small world networks: Experimental evidence. Games and Economic Behavior, 58(2007), 209–230.CrossRefGoogle Scholar
  7. Cressman, R. (2003). Evolutionary dynamics and extensive form games. Cambridge, USA: MIT Press.Google Scholar
  8. Durán, O., & Mulet, R. (2005). Evolutionary prisoner’s dilemma in random graphs. Physica D: Nonlinear Phenomena, 208(3–4), 257–265.CrossRefGoogle Scholar
  9. Ebel, H., & Bornholdt, S. (2002). Coevolutionary games on networks. Physical Review E, 66, 056118.CrossRefGoogle Scholar
  10. Gintis, H. (2000). Game theory evolving. Princeton, USA: Princeton University Press.Google Scholar
  11. Hauert, C., & Doebeli, M. (2004). Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature, 428, 643–646.CrossRefGoogle Scholar
  12. Jackson, M. O., & Watts, A. (2002). On the formation of interaction networks in social coordination games. Games and Economic Behavior, 41, 265–291.CrossRefGoogle Scholar
  13. Kleinberg, J. (2007). Cascading behavior in networks: Algorithmic and economic issues. In N. Nisan, T. Roughgarden, E. Tardos, & V. Vazirani (Eds.), Algorithmic game theory. Cambridge, USA: Cambridge University Press.Google Scholar
  14. Kollock, P. (1998). Social dilemmas: The anatomy of cooperation. Annual Review of Sociology, 24, 183–214.CrossRefGoogle Scholar
  15. Lieberman, E., Hauert, C., & Nowak, M. A. (2005). Evolutionary dynamics on graphs. Nature, 433, 312–316.CrossRefGoogle Scholar
  16. Masuda, N. (2003). Spatial prisoner’s dilemma optimally played in small-world networks. Physics Letters A, 313(1–2), 55–61.CrossRefGoogle Scholar
  17. Nowak, M. A., & Sigmund, K. (2005). Evolution of indirect reciprocity. Nature, 437, 1291–1298.CrossRefGoogle Scholar
  18. Ohtsuki, H., Hauert, C., Lieberman, E., & Nowak, M. (2006). A simple rule for the evolution of cooperation on graph and social networks. Nature, 441, 502–505.CrossRefGoogle Scholar
  19. Ohtsuki, H., Pacheco, J., & Nowak, M. A. (2007). Evolutionary graph theory: Breaking the symmetry between interaction and replacement. Journal of Theoretical Biology, 246, 681–694.CrossRefGoogle Scholar
  20. Ostrom, E. (1990). Governing the commons: The evolution of institutions for collective action. Cambridge, USA: Cambridge University Press.CrossRefGoogle Scholar
  21. Pacheco, J. M., Traulsen, A., & Nowak, M. A. (2006). Coevolution of strategy and structure in complex networks with dynamical linking. Physical Review Letters, 97(25), 25810.CrossRefGoogle Scholar
  22. Roca, C. P., Cuesta, J. A., & Sa’nchez, A. (2009). Effect of spatial structure on the evolution of cooperation. Physical Review E, 80(4), 046106.CrossRefGoogle Scholar
  23. Santos, F. C., Pacheco, J. M., & Lenaerts, T. (2006a). Evolutionary dynamics of social dilemmas in structured heterogeneous populations. PNAS, 103(9), 3490–3494.CrossRefGoogle Scholar
  24. Santos, F. C., Pacheco, J. M., & Lenaerts, T. (2006b). Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proceedings of the National Academy of Sciences of the USA, 103(3), 490-349.Google Scholar
  25. Santos, F. C., Santos, M. D., & Pacheco, J. M. (2008). Social diversity promotes the emergence of cooperation in public goods games. Nature, 454, 213–216.CrossRefGoogle Scholar
  26. Science (2005). 309(5731), 78–102. doi: 10.1126/science.309.5731.78b.
  27. Sigmund, K. (1993). Games of life. Oxford, UK: Oxford University Press.Google Scholar
  28. Sood, V., Antal, T., & Redner, S. (2008). Voter models on heterogeneous networks. Physical Review E, 77, 041121.CrossRefGoogle Scholar
  29. Suzuki, R, Arita, T (2009). Evolution of Cooperation on Different Pairs of Interaction and Replacement Networks with Various Intensity of Selection.In IEEE Congress on Evolutionary Computation, 494–499.Google Scholar
  30. Szolnoki, A., Perc, M., & Danku, Z. (2008). Towards effective payoffs in the prisoner’s dilemma game on scale-free networks. Physica A, 387, 2075.CrossRefGoogle Scholar
  31. Taylor, P. D., Day, T., & Wild, G. (2007). Evolution of cooperation in a finite homogeneous graph. Nature, 447(7143), 469–472.CrossRefGoogle Scholar
  32. Vukov, J., Szab’o, G., & Szolnoki, A. (2008). Evolutionary prisoner’s dilemma game on the Newman-Watts networks. Physical Review E, 77, 026109.CrossRefGoogle Scholar
  33. Watts, D. (1999). Small world: The dynamics of networks between order and randomness. Princeton, USA: Princeton University Press.Google Scholar
  34. Weibull, J. (1997). Evolutionary game theory. Cambridge, USA: MIT Press.Google Scholar
  35. Wilensky, U. (2005). NetLogo Preferential Attachment model... Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL. http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment. Accessed Sep 23 2012.
  36. Wu, Z.-X., & Wang, Y.-H. (2007). Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner’s dilemma games. Physical Review E, 75(4), 0411.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Economics and Business StudiesUniversity of BremenBremenGermany

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