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Co-evolutionary dynamics and Bayesian interaction games

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  • Mathias Staudigl

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Abstract

Recently there has been a growing interest in evolutionary models of play with endogenous interaction structure. We call such processes co-evolutionary dynamics of networks and play. We study a co-evolutionary process of networks and play in settings where players have diverse preferences. In the class of potential games we provide a closed-form solution for the unique invariant distribution of this process. Based on this result we derive various asymptotic statistics generated by the co-evolutionary process. We give a complete characterization of the random graph model, and stochastically stable states in the small noise limit. Thereby we can select among action profiles and networks which appear jointly with non-vanishing frequency in the limit of small noise in the population. We further study stochastic stability in the limit of large player populations. Copyright Springer-Verlag 2013

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 42 (2013)
Issue (Month): 1 (February)
Pages: 179-210

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Handle: RePEc:spr:jogath:v:42:y:2013:i:1:p:179-210

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Related research

Keywords: Potential games; Network evolution; Heterogeneous populations; Inhomogeneous random graphs; Large deviations;

References

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  1. J. Scheinkman & U. Horst, 2003. "Equilibria in Systems of Social Interactions," Princeton Economic Theory Working Papers d5a39039d26e0b08775b915bf, David K. Levine.
  2. Ely, Jeffrey C. & Sandholm, William H., 2005. "Evolution in Bayesian games I: Theory," Games and Economic Behavior, Elsevier, vol. 53(1), pages 83-109, October.
  3. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
  4. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  5. Sanjeev Goyal & Fernando Vega-Redondo, 2003. "Network Formation and Social Coordination," Working Papers 481, Queen Mary, University of London, School of Economics and Finance.
  6. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
  7. Staudigl, Mathias, 2011. "Potential games in volatile environments," Games and Economic Behavior, Elsevier, vol. 72(1), pages 271-287, May.
  8. Hofbauer,J. & Sandholm,W.H., 2003. "Evolution in games with randomly disturbed payoffs," Working papers 20, Wisconsin Madison - Social Systems.
  9. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  10. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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Cited by:
  1. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
  2. Staudigl, Mathias, 2011. "Potential games in volatile environments," Games and Economic Behavior, Elsevier, vol. 72(1), pages 271-287, May.
  3. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.

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