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Potential games in volatile environments

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  • Staudigl, Mathias

Abstract

This paper studies the co-evolution of networks and play in the context of finite population potential games. Action revision, link creation and link destruction are combined in a continuous-time Markov process. I derive the unique invariant distribution of this process in closed form, as well as the marginal distribution over action profiles and the conditional distribution over networks. It is shown that the equilibrium interaction topology is an inhomogeneous random graph. Furthermore, a characterization of the set of stochastically stable states is provided, generalizing existing results to models with endogenous interaction structures.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 72 (2011)
Issue (Month): 1 (May)
Pages: 271-287

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Handle: RePEc:eee:gamebe:v:72:y:2011:i:1:p:271-287

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Markov process Potential game Stochastic stability Network co-evolution Random graphs;

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References

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  1. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
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  9. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
  10. David P. Myatt & Chris Wallace, 2002. "A Multinomial Probit Model of Stochastic Evolution," Economics Series Working Papers 90, University of Oxford, Department of Economics.
  11. Matthew O. Jackson & Alison Watts, 2000. "On the Formation of Interaction Networks in Social Coordination Games," Econometric Society World Congress 2000 Contributed Papers 0778, Econometric Society.
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  13. Hojman, Daniel A. & Szeidl, Adam, 2006. "Endogenous networks, social games, and evolution," Games and Economic Behavior, Elsevier, vol. 55(1), pages 112-130, April.
  14. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096.
  15. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
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  18. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  19. George Ehrhardt & Matteo Marsili & Fernando Vega-Redondo, 2008. "Networks Emerging in a Volatile World," Economics Working Papers ECO2008/08, European University Institute.
  20. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
  21. Mathias Staudigl, 2013. "Co-evolutionary dynamics and Bayesian interaction games," International Journal of Game Theory, Springer, vol. 42(1), pages 179-210, February.
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Citations

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Cited by:
  1. Mathias Staudigl & Simon Weidenholzer, 2010. "Constrained Interactions and Social Coordination," Vienna Economics Papers 1004, University of Vienna, Department of Economics.
  2. Tim Hellmann & Mathias Staudigl, 2012. "Evolution of social networks," Working Papers 470, Bielefeld University, Center for Mathematical Economics.
  3. Mathias Staudigl, 2013. "Co-evolutionary dynamics and Bayesian interaction games," International Journal of Game Theory, Springer, vol. 42(1), pages 179-210, February.
  4. König, Michael & Tessone, Claudio J. & Zenou, Yves, 2012. "Nestedness in Networks: A Theoretical Model and Some Applications," CEPR Discussion Papers 8807, C.E.P.R. Discussion Papers.
  5. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
  6. Xiaodong Liu & Eleonora Patacchini & Yves Zenou & Lung-Fei Lee, 2012. "Criminal Networks: Who is the Key Player?," Working Papers 2012.39, Fondazione Eni Enrico Mattei.
  7. Roland Pongou & Roberto Serrano, 2013. "Volume of Trade and Dynamic Network Formation in Two-Sided Economies," Working Papers 2013-6, Brown University, Department of Economics.
  8. Pongou, Roland & Serrano, Roberto, 2013. "Dynamic Network Formation in Two-Sided Economies," MPRA Paper 46021, University Library of Munich, Germany.
  9. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 551-585, November.

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