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

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  • 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
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    References listed on IDEAS

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    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.
    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.
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    Cited by:

    1. Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
    2. 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.
    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.

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    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

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