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Nash Equilibrium and Robust Stability in Dynamic Games: A Small-Gain Perspective

Author

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  • Karafyllis, Iasson
  • Jiang, Zhong-Ping
  • Athanasiou, George

Abstract

This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions guaranteeing uniqueness and global asymptotic stability of Nash equilibrium point for economic models described by functional difference equations. Specification to a Cournot oligopoly game is studied in detail to demonstrate the power of the proposed methodology.

Suggested Citation

  • Karafyllis, Iasson & Jiang, Zhong-Ping & Athanasiou, George, 2010. "Nash Equilibrium and Robust Stability in Dynamic Games: A Small-Gain Perspective," MPRA Paper 26890, University Library of Munich, Germany, revised 23 Sep 2010.
    • Handle: RePEc:pra:mprapa:26890
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    File URL: https://mpra.ub.uni-muenchen.de/26890/1/MPRA_paper_26890.pdf
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    References listed on IDEAS

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    1. Szidarovszky, Ferenc & Li, Weiye, 2000. "A note on the stability of a Cournot-Nash equilibrium: the multiproduct case with adaptive expectations," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 101-107, February.
    2. Hommes, Cars H., 1998. "On the consistency of backward-looking expectations: The case of the cobweb," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 333-362, January.
    3. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    4. Chiarella, Carl & Szidarovszky, Ferenc, 2004. "Dynamic oligopolies without full information and with continuously distributed time lags," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 495-511, August.
    5. Huang, Weihong, 2008. "Information lag and dynamic stability," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 513-529, April.
    6. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    7. Athanasiou, George & Karafyllis, Iasson & Kotsios, Stelios, 2008. "Price stabilization using buffer stocks," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1212-1235, April.
    8. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    9. Nabih Agiza, Hamdy & Italo Bischi, Gian & Kopel, Michael, 1999. "Multistability in a dynamic Cournot game with three oligopolists," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(1), pages 63-90.
    10. Okuguchi, Koji & Yamazaki, Takeshi, 2008. "Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1204-1211, April.
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    Cited by:

    1. Ryoichi Nishimura & Shunsuke Hayashi & Masao Fukushima, 2012. "Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets," Journal of Global Optimization, Springer, vol. 53(1), pages 107-120, May.
    2. Qian Zhao & Lian-ying Zhang, 2018. "Research on the Effect of DPSO in Team Selection Optimization under the Background of Big Data," Complexity, Hindawi, vol. 2018, pages 1-14, July.

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    More about this item

    Keywords

    Dynamic game; Cournot oligopoly; Nash equilibrium; Robust stability; Small gain;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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