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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.

Suggested Citation

  • Staudigl, Mathias, 2011. "Potential games in volatile environments," Games and Economic Behavior, Elsevier, vol. 72(1), pages 271-287, May.
    • Handle: RePEc:eee:gamebe:v:72:y:2011:i:1:p:271-287
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    References listed on IDEAS

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    1. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406.
    2. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    3. 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.
    4. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
    8. Mathias Staudigl, 2013. "Co-evolutionary dynamics and Bayesian interaction games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 179-210, February.
    9. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.
    10. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
    11. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    12. 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.
    13. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
    14. George Ehrhardt & Matteo Marsili & Fernando Vega-Redondo, 2008. "Networks Emerging in a Volatile World," Economics Working Papers ECO2008/08, European University Institute.
    15. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    16. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
    17. Myatt, David P. & Wallace, Chris, 2003. "A multinomial probit model of stochastic evolution," Journal of Economic Theory, Elsevier, vol. 113(2), pages 286-301, December.
    18. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096.
    19. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    20. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    21. Hojman, Daniel A. & Szeidl, Adam, 2006. "Endogenous networks, social games, and evolution," Games and Economic Behavior, Elsevier, vol. 55(1), pages 112-130, April.
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    Cited by:

    1. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    2. Anton Badev, 2014. "Discrete Games in Endogenous Networks: Theory and Policy," 2014 Meeting Papers 901, Society for Economic Dynamics.
    3. Markus Kinateder & Luca Paolo Merlino, 2021. "The Evolution of Networks and Local Public Good Provision: A Potential Approach," Games, MDPI, vol. 12(3), pages 1-12, July.
    4. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves & Lee, Lung-Fei, 2011. "Criminal Networks: Who is the Key Player?," Research Papers in Economics 2011:7, Stockholm University, Department of Economics.
    5. Staudigl, Mathias & Weidenholzer, Simon, 2014. "Constrained interactions and social coordination," Journal of Economic Theory, Elsevier, vol. 152(C), pages 41-63.
    6. Zhiwei Cui, 2019. "Matching, Imitation, and Coordination in Networks," Dynamic Games and Applications, Springer, vol. 9(1), pages 47-67, March.
    7. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    8. Pongou, Roland & Serrano, Roberto, 2016. "Volume of trade and dynamic network formation in two-sided economies," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 147-163.
    9. Péter Bayer & Ani Guerdjikova, 2020. "Optimism leads to optimality: Ambiguity in network formation," Working Papers hal-03005107, HAL.
    10. Mathias Staudigl, 2013. "Co-evolutionary dynamics and Bayesian interaction games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 179-210, February.
    11. Sawa, Ryoji, 2021. "A stochastic stability analysis with observation errors in normal form games," Games and Economic Behavior, Elsevier, vol. 129(C), pages 570-589.
    12. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
    13. Pongou, Roland & Serrano, Roberto, 2013. "Dynamic Network Formation in Two-Sided Economies," MPRA Paper 46021, University Library of Munich, Germany.
    14. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    15. repec:esx:essedp:747 is not listed on IDEAS

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