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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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    1. 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).
    2. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    3. 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.
    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, October.
    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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