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A Numerical Algorithm to Calculate the Unique Feedback Nash Equilibrium in a Large Scalar LQ Differential Game

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  • Jacob Engwerda

    (Tilburg University)

Abstract

In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0201-7
    DOI: 10.1007/s13235-016-0201-7
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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. 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.
    4. 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, July-Dece.
    5. 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.
    6. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    7. Tamer Başar & Quanyan Zhu, 2011. "Prices of Anarchy, Information, and Cooperation in Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 50-73, March.
    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.
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    Cited by:

    1. Bolei Di & Andrew Lamperski, 2022. "Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games," Dynamic Games and Applications, Springer, vol. 12(2), pages 394-442, June.
    2. Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.

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