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

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

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.

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File URL: http://mpra.ub.uni-muenchen.de/26890/1/MPRA_paper_26890.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26890.

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Date of creation: 07 Jan 2010
Date of revision: 23 Sep 2010
Publication status: Published in Computers and Mathematics with Applications 11.60(2010): pp. 2936-2952
Handle: RePEc:pra:mprapa:26890
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Web page: http://mpra.ub.uni-muenchen.de

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  1. Huang, Weihong, 2008. "Information lag and dynamic stability," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 513-529, April.
  2. 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.
  3. 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.
  4. 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.
  5. Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. J. E. Stiglitz, 1999. "Introduction," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 28(3), pages 249-254, November.
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