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Cournot tatonnement and potentials

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  • Kukushkin, Nikolai S.

Abstract

We study what topological assumptions should be added to the acyclicity of individual best response improvements in order to ensure the existence of a (pure strategy) Nash equilibrium in a strategic game, as well as the possibility to reach a Nash equilibrium in the limit of a best response improvement path.

Suggested Citation

  • Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    • Handle: RePEc:eee:mateco:v:59:y:2015:i:c:p:117-127
    DOI: 10.1016/j.jmateco.2015.06.005
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    References listed on IDEAS

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    1. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    2. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    3. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
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    7. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    8. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    9. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    10. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    11. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    13. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    14. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 45-66, April.
    15. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    16. Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
    17. Francisco Facchinei & Veronica Piccialli & Marco Sciandrone, 2011. "Decomposition algorithms for generalized potential games," Computational Optimization and Applications, Springer, vol. 50(2), pages 237-262, October.
    18. Kukushkin Nikolai S., 1994. "A Condition for the Existence of a Nash Equilibrium in Games with Public and Private Objectives," Games and Economic Behavior, Elsevier, vol. 7(2), pages 177-192, September.
    19. Nikolai S Kukushkin, 2004. "'Strategic supplements' in games with polylinear interactions," Game Theory and Information 0411008, University Library of Munich, Germany, revised 28 Feb 2005.
    20. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    21. Nikolai Kukushkin, 2011. "Nash equilibrium in compact-continuous games with a potential," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 387-392, May.
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    Citations

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    Cited by:

    1. Bervoets, Sebastian & Faure, Mathieu, 2019. "Stability in games with continua of equilibria," Journal of Economic Theory, Elsevier, vol. 179(C), pages 131-162.
    2. Péter Bayer & György Kozics & Nóra Gabriella Szőke, 2020. "Best-Response Dynamics in Directed Network Games," CEU Working Papers 2020_1, Department of Economics, Central European University.
    3. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald & Thuijsman, Frank, 2019. "Adaptive learning in weighted network games," Journal of Economic Dynamics and Control, Elsevier, vol. 105(C), pages 250-264.
    4. Nikolai S. Kukushkin & Pierre von Mouche, 2018. "Cournot tatonnement and Nash equilibrium in binary status games," Economics Bulletin, AccessEcon, vol. 38(2), pages 1038-1044.
    5. P'eter Bayer & Gyorgy Kozics & N'ora Gabriella SzH{o}ke, 2021. "Best-response dynamics in directed network games," Papers 2101.03863, arXiv.org.

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    More about this item

    Keywords

    Cournot tatonnement; Cournot potential; Game with structured utilities; Aggregative game;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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