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The Open-Loop Discounted Linear Quadratic Differential Game for Regular Higher Order Index Descriptor Systems


  • Engwerda, J.C.

    (Tilburg University, Center For Economic Research)

  • Salmah, Y.
  • Wijayanti, I.E.


In this paper we consider the discounted linear quadratic differential game for descriptor systems that have an index larger than one. We derive both necessary and sufficient conditions for existence of an open-loop Nash (OLN) equilibrium. In a small macro-economic stabilization game we illustrate that the corresponding optimal response is generically cyclic.

Suggested Citation

  • Engwerda, J.C. & Salmah, Y. & Wijayanti, I.E., 2009. "The Open-Loop Discounted Linear Quadratic Differential Game for Regular Higher Order Index Descriptor Systems," Discussion Paper 2009-1, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:fb9d053c-a681-4b7e-9fdc-8910adaa3fca

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    References listed on IDEAS

    1. Engwerda, J.C., 2008. "Uniqueness conditions for the affine open-loop linear quadratic differential games," Other publications TiSEM 53b6b5ec-5e13-4805-8d09-9, Tilburg University, School of Economics and Management.
    2. Engwerda, J.C. & Salmah, Y. & Wijayanti, I.E., 2008. "The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems," Discussion Paper 2008-90, Tilburg University, Center for Economic Research.
    3. 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, December.
    4. Reinhard Neck & Engelbert Dockner, 1995. "Commitment and coordination in a dynamic game model of international economic policy-making," Open Economies Review, Springer, vol. 6(1), pages 5-28, January.
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    Cited by:

    1. Reddy, P.V. & Engwerda, J.C., 2010. "Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors," Discussion Paper 2010-140, Tilburg University, Center for Economic Research.
    2. 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.
    3. 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.

    More about this item


    linear quadratic differential games; open-loop information structure; descriptor systems;

    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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