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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. 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.
    2. 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.
    3. Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.
    4. 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.
    5. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
    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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