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Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine-Quadratic Differential Game

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  • J. C. Engwerda

    (Tilburg University)

  • Salmah

    (Gadjah Mada University)

Abstract

In this note, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium. As a special case, we derive existence conditions for the multi-player zero-sum game.

Suggested Citation

  • J. C. Engwerda & Salmah, 2013. "Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine-Quadratic Differential Game," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 552-563, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0188-1
    DOI: 10.1007/s10957-012-0188-1
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    References listed on IDEAS

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    1. Jacob Engwerda, 2007. "Algorithms for computing Nash equilibria in deterministic LQ games," Computational Management Science, Springer, vol. 4(2), pages 113-140, April.
    2. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
    3. W. A. van den Broek & J. C. Engwerda & J. M. Schumacher, 2003. "Robust Equilibria in Indefinite Linear-Quadratic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 565-595, December.
    4. Weeren, A.J.T.M. & Schumacher, J.M. & Engwerda, J.C., 1994. "Asymptotic analysis of Nash equilibria in nonzero-sum linear-quadratic differential games : The two player case," Research Memorandum FEW 634, Tilburg University, School of Economics and Management.
    5. Joseph Plasmans & Jacob Engwerda & Bas van Aarle & Giovanni di Bartolomeo & Tomasz Michalak, 2006. "Dynamic Modeling of Monetary and Fiscal Cooperation Among Nations," Dynamic Modeling and Econometrics in Economics and Finance, Springer, number 978-0-387-27931-2, June.
    6. Engwerda, J.C. & Weeren, A.J.T.M., 2006. "A Result on Output Feedback Linear Quadratic Control," Other publications TiSEM a11b5333-1364-4a3c-a637-4, Tilburg University, School of Economics and Management.
    7. 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.
    8. 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, November.
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    Cited by:

    1. Engwerda, J.C., 2013. "A Numerical Algorithm to find All Scalar Feedback Nash Equilibria," Discussion Paper 2013-050, Tilburg University, Center for Economic Research.
    2. Jacob Engwerda, 2017. "A Numerical Algorithm to Calculate the Unique Feedback Nash Equilibrium in a Large Scalar LQ Differential Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 635-656, December.
    3. 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.

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