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On a Constrained Infinite-Time Horizon Linear Quadratic Game

Author

Listed:
  • Mikhail I. Krastanov

    (Sofia University
    Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)

  • Rossen Rozenov

    (International Monetary Fund)

  • Boyan K. Stefanov

    (Sofia University
    Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)

Abstract

A linear quadratic differential game on an infinite-time horizon is studied in the case when the controls of the minimizing player are subject to constraints. A sufficient condition for a saddle point equilibrium is provided based on the conversion of the infinite-time horizon game to a game on a finite-time horizon. The method is applied to a simple monetary policy model as an illustrative example.

Suggested Citation

  • Mikhail I. Krastanov & Rossen Rozenov & Boyan K. Stefanov, 2023. "On a Constrained Infinite-Time Horizon Linear Quadratic Game," Dynamic Games and Applications, Springer, vol. 13(3), pages 843-858, September.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00484-6
    DOI: 10.1007/s13235-022-00484-6
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    References listed on IDEAS

    as
    1. S. J. Rubio, 2006. "On Coincidence of Feedback Nash Equilibria and Stackelberg Equilibria in Economic Applications of Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 203-220, January.
    2. Dennis, Richard & Leitemo, Kai & Söderström, Ulf, 2009. "Methods for robust control," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1604-1616, August.
    3. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
    4. Marc P. Giannoni, 2007. "Robust optimal monetary policy in a forward-looking model with parameter and shock uncertainty," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 179-213.
    5. Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.
    6. 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.
    7. Michael Woodford, 2003. "Optimal Interest-Rate Smoothing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(4), pages 861-886.
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    More about this item

    Keywords

    Differential games; Linear quadratic optimal control; Model uncertainty; Robustness;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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