Nash Equilibrium and Robust Stability in Dynamic Games: A Small-Gain Perspective
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.
|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|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Huang, Weihong, 2008. "Information lag and dynamic stability," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 513-529, April.
- J. E. Stiglitz, 1999. "Introduction," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 28(3), pages 249-254, November. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:26890. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.