IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v117y2003i2d10.1023_a1023699021996.html
   My bibliography  Save this article

On the Selection of One Feedback Nash Equilibrium in Discounted Linear-Quadratic Games

Author

Listed:
  • P. Cartigny

    (Université de la Méditerranée)

  • P. Michel

    (Université de la Méditerranée)

Abstract

We study a selection method for a Nash feedback equilibrium of a one-dimensional linear-quadratic nonzero-sum game over an infinite horizon. By introducing a change in the time variable, one obtains an associated game over a finite horizon T > 0 and with free terminal state. This associated game admits a unique solution which converges to a particular Nash feedback equilibrium of the original problem as the horizon T goes to infinity.

Suggested Citation

  • P. Cartigny & P. Michel, 2003. "On the Selection of One Feedback Nash Equilibrium in Discounted Linear-Quadratic Games," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 231-243, May.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:2:d:10.1023_a:1023699021996
    DOI: 10.1023/A:1023699021996
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1023699021996
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1023699021996?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    2. A. J. T. M. Weeren & J. M. Schumacher & J. C. Engwerda, 1999. "Asymptotic Analysis of Linear Feedback Nash Equilibria in Nonzero-Sum Linear-Quadratic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 693-722, June.
    3. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
    5. Engwerda, J.C., 2000. "Feedback Nash equilibria in the scalar infinite horizon LQ-Game," Other publications TiSEM 58ccf964-4ca1-4d67-9a68-a, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Denis Claude & Charles Figuières & Mabel Tidball, 2012. "Regulation of Investments in Infrastructure: The Interplay between Strategic Behaviors and Initial Endowments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(1), pages 35-66, February.
    2. Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
    3. Javier Frutos & Guiomar Martín-Herrán, 2018. "Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games," Dynamic Games and Applications, Springer, vol. 8(3), pages 620-636, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Halkos, George & Papageorgiou, George, 2015. "Dynamical methods in Environmental and Resource Economics," MPRA Paper 67845, University Library of Munich, Germany.
    2. Engwerda, J.C., 2013. "A Numerical Algorithm to find All Scalar Feedback Nash Equilibria," Other publications TiSEM aa391d31-11df-4693-9583-1, Tilburg University, School of Economics and Management.
    3. Berthod, Mathias & Benchekroun, Hassan, 2019. "On agreements in a nonrenewable resource market: A cooperative differential game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 23-39.
    4. Naïla Hayek, 2011. "A Generalization of Mixed Problems with an Application to Multiobjective Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 498-515, September.
    5. Alberto Bressan & Khai T. Nguyen, 2018. "Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 42-78, March.
    6. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    7. Sergey Aseev & Gernot Hutschenreiter & Arkadii V. Kryazhimskii, 2002. "Optimal Investment in R&D with International Knowledge Spillovers," WIFO Working Papers 175, WIFO.
    8. Ravi Kashyap, 2016. "Solving the Equity Risk Premium Puzzle and Inching Towards a Theory of Everything," Papers 1604.04872, arXiv.org, revised Sep 2019.
    9. Stefano Bosi & Carmen Camacho & David Desmarchelier, 2023. "Human capital and welfare," PSE-Ecole d'économie de Paris (Postprint) halshs-03920429, HAL.
    10. Stefano Bosi & Carmen Camacho & David Desmarchelier, 2020. "Human capital and welfare," PSE Working Papers halshs-02482543, HAL.
    11. Allise O. Wachs & Irwin E. Schochetman & Robert L. Smith, 2011. "Average Optimality in Nonhomogeneous Infinite Horizon Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 147-164, February.
    12. Feichtinger, Gustav & Grass, Dieter & Kort, Peter M. & Seidl, Andrea, 2021. "On the Matthew effect in research careers," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    13. Chen Ling & Michael Caputo, 2012. "The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 313-334, September.
    14. Engwerda, J.C., 1996. "The Infinite Horizon Open-Loop Nash LQ-Game," Other publications TiSEM bb9762e7-faab-4ad2-8dd8-4, Tilburg University, School of Economics and Management.
    15. Jean-Bernard Chatelain & Bruno Tinel & Karim Azizi & Nicolas Canry, 2012. "Are the No-Ponzi Game and the Transversality Conditions Relevant for Public Debt? A Keynesian Appraisal," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00686788, HAL.
    16. Mojtaba Dehghan Banadaki & Hamidreza Navidi, 2020. "Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method," Games, MDPI, vol. 11(3), pages 1-11, July.
    17. Azizi, Karim & Canry, Nicolas & Chatelain, Jean-Bernard & Tinel, Bruno, 2013. "Government Solvency, Austerity and Fiscal Consolidation in the OECD: A Keynesian Appraisal of Transversality and No Ponzi Game Conditions," EconStor Preprints 72550, ZBW - Leibniz Information Centre for Economics.
    18. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    19. Engwerda, J.C., 1999. "The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations," Other publications TiSEM 63f19390-d8dd-4c84-9b96-7, Tilburg University, School of Economics and Management.
    20. Gordon, Sidartha & Marlats, Chantal & Ménager, Lucie, 2021. "Observation delays in teams and effort cycles," Games and Economic Behavior, Elsevier, vol. 130(C), pages 276-298.

    More about this item

    Keywords

    Linear-quadratic games; nonzero-sum differential games; Nash equilibria; infinite-horizon problems;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:117:y:2003:i:2:d:10.1023_a:1023699021996. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.