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Algorithms for computing Nash equilibria in deterministic LQ games

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  • Jacob Engwerda

Abstract

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.
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Suggested Citation

  • Jacob Engwerda, 2007. "Algorithms for computing Nash equilibria in deterministic LQ games," Computational Management Science, Springer, vol. 4(2), pages 113-140, April.
    • Handle: RePEc:spr:comgts:v:4:y:2007:i:2:p:113-140
    DOI: 10.1007/s10287-006-0030-z
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    References listed on IDEAS

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    1. 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, March.
    2. Tomasz Michalak & Jacob Engwerda & Joseph Plasmans, 2011. "A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games," Computational Economics, Springer;Society for Computational Economics, vol. 37(4), pages 375-410, April.
    3. Reinganum, Jennifer F & Stokey, Nancy L, 1985. "Oligopoly Extraction of a Common Property Natural Resource: The Importance of the Period of Commitment in Dynamic Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 161-173, February.
    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. van den Broek, W.A. & Engwerda, J.C. & Schumacher, J.M., 2003. "An equivalence result in linear-quadratic theory," Other publications TiSEM d65171ce-101d-4204-a1ec-f, Tilburg University, School of Economics and Management.
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    1. 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.
    2. Engwerda, Jacob, 2017. "A numerical algorithm to calculate the unique feedback nash equilibrium in a large scalar LQ differential game," Other publications TiSEM 0442b203-1b92-4be3-ba60-7, Tilburg University, School of Economics and Management.
    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. Eigruber, Markus & Wirl, Franz, 2024. "Market equilibrium strategies under learning by doing and spillovers," Energy Economics, Elsevier, vol. 131(C).
    5. Engwerda, J. & Boldea, O. & Michalak, T. & Plasmans, J. & Salmah,, 2012. "A simulation study of an ASEAN monetary union," Economic Modelling, Elsevier, vol. 29(5), pages 1870-1890.
    6. 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.
    7. Tomasz Michalak & Jacob Engwerda & Joseph Plasmans, 2011. "A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games," Computational Economics, Springer;Society for Computational Economics, vol. 37(4), pages 375-410, April.
    8. Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.
    9. Engwerda, J.C., 2013. "A Numerical Algorithm to find All Scalar Feedback Nash Equilibria," Discussion Paper 2013-050, Tilburg University, Center for Economic Research.

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    More about this item

    Keywords

    Algebraic Riccati equations; Linear quadratic differential games; Nash equilibria;
    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
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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