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Robust Equilibria in Indefinite Linear-Quadratic Differential Games

Author

Listed:
  • W. A. van den Broek

    (University of Twente)

  • J. C. Engwerda

    (Tilburg University)

  • J. M. Schumacher

    (University of Twente)

Abstract

Equilibria in dynamic games are formulated often under the assumption that the players have full knowledge of the dynamics to which they are subject. Here, we formulate equilibria in which players are looking for robustness and take model uncertainty explicitly into account in their decisions. Specifically, we consider feedback Nash equilibria in indefinite linear-quadratic differential games on an infinite time horizon. Model uncertainty is represented by a malevolent input which is subject to a cost penalty or to a direct bound. We derive conditions for the existence of robust equilibria in terms of solutions of sets of algebraic Riccati equations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006690.78564.88
    DOI: 10.1023/B:JOTA.0000006690.78564.88
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    References listed on IDEAS

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    1. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    2. van den Broek, W.A., 2001. "Uncertainty in differential games," Other publications TiSEM 195bcb68-8943-49c1-8acb-0, 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," Discussion Paper 2013-050, Tilburg University, Center for Economic Research.
    2. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi & Ted Loch-Temzelides & Cristiano Ricci, 2025. "An integral transformation approach to differential games: a climate model application," LIDAM Discussion Papers IRES 2025001, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. I. Ivanov & Lars Imsland & B. Bogdanova, 2017. "Iterative algorithms for computing the feedback Nash equilibrium point for positive systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 729-737, March.
    4. Engwerda, J.C. & Salmah, Y., 2010. "Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games," Discussion Paper 2010-79, Tilburg University, Center for Economic Research.
    5. Engwerda, J.C. & Salmah, Y., 2010. "Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential," Other publications TiSEM 4be56827-dca1-42c3-8872-6, Tilburg University, School of Economics and Management.
    6. 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.
    7. Engwerda, J.C., 2004. "A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games," Other publications TiSEM 7a3232f4-ef03-4cc7-a438-e, Tilburg University, School of Economics and Management.
    8. Engwerda, Jacob, 2017. "Stabilization of an Uncertain Simple Fishery Management Game," Discussion Paper 2017-031, Tilburg University, Center for Economic Research.
    9. Yiyong Cai & Warwick McKibbin, 2015. "Uncertainty and International Climate Change Negotiations," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 1(1), pages 101-115, March.
    10. Muhammad Wakhid Musthofa & Salmah & Jacob Engwerda & Ari Suparwanto, 2016. "Robust Optimal Control Design Using a Differential Game Approach for Open-Loop Linear Quadratic Descriptor Systems," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1046-1064, March.
    11. Engwerda, J.C., 2012. "Prospects of Tools from Differential Games in the Study Of Macroeconomics of Climate Change," Discussion Paper 2012-045, Tilburg University, Center for Economic Research.
    12. Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.
    13. Engwerda, J.C., 2005. "Uncertainty in a Fishery Management Game," Other publications TiSEM 79d94d3b-4953-4511-9674-f, Tilburg University, School of Economics and Management.
    14. Bingyan Han & Chi Seng Pun & Hoi Ying Wong, 2023. "Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach," Papers 2306.16982, arXiv.org, revised Sep 2024.

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