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Potential games in volatile environments

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Abstract

This papers 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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File URL: http://homepage.univie.ac.at/Papers.Econ/RePEc/vie/viennp/vie1002.pdf
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Paper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 1002.

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Date of creation: Feb 2010
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Handle: RePEc:vie:viennp:1002

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  1. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, vol. 41(2), pages 265-291, November.
  2. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
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  4. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
  5. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
  6. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
  7. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  8. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  9. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers 1394, Cowles Foundation for Research in Economics, Yale University.
  10. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  11. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
  12. Sanjeev Goyal & Fernando Vega-Redondo, 2003. "Network Formation and Social Coordination," Working Papers 481, Queen Mary, University of London, School of Economics and Finance.
  13. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096, October.
  14. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  15. Hojman, Daniel A. & Szeidl, Adam, 2006. "Endogenous networks, social games, and evolution," Games and Economic Behavior, Elsevier, vol. 55(1), pages 112-130, April.
  16. David P. Myatt & Chris Wallace, 2002. "A Multinomial Probit Model of Stochastic Evolution," Economics Series Working Papers 90, University of Oxford, Department of Economics.
  17. George Ehrhardt & Matteo Marsili & Fernando Vega-Redondo, 2008. "Networks Emerging in a Volatile World," Economics Working Papers ECO2008/08, European University Institute.
  18. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  19. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  20. 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. 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.
  2. 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.
  3. Mathias Staudigl & Simon Weidenholzer, 2010. "Constrained Interactions and Social Coordination," Vienna Economics Papers 1004, University of Vienna, Department of Economics.
  4. Michael Koenig & Claudio Tessone & Yves Zenou, 2012. "Nestedness in Networks: A Theoretical Model and Some Applications," Discussion Papers 11-003, Stanford Institute for Economic Policy Research.
  5. 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.
  6. Pongou, Roland & Serrano, Roberto, 2013. "Dynamic Network Formation in Two-Sided Economies," MPRA Paper 46021, University Library of Munich, Germany.
  7. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
  8. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
  9. 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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