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The Linear Quadratic Dynamic Game For Discrete-Time Descriptor Systems

Author

Listed:
  • HUA XU

    (Graduate School of Business Sciences, The University of Tsukuba, Tokyo, 3-29-1 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan)

  • HIROAKI MUKAIDANI

    (Graduate School of Education, Hiroshima University, 1-1-1, Kagamiyama, Higashi-Hiroshima, 739-8524, Japan)

Abstract

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to find the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a Hamiltonian matrix, are given such that the linear quadratic zero-sum dynamic game for the reduced-order discrete time state space system is available. Sufficient conditions for the existence of the solutions are obtained. In contrast with the dynamic game in state space systems, the dynamic game in descriptor systems admits uncountably many linear feedback saddle-point solutions. All these solutions have the same existence conditions and achieve the same value of the dynamic game.

Suggested Citation

  • Hua Xu & Hiroaki Mukaidani, 2003. "The Linear Quadratic Dynamic Game For Discrete-Time Descriptor Systems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 361-374.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:04:n:s0219198903001100
    DOI: 10.1142/S0219198903001100
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    More about this item

    Keywords

    Descriptor systems; dynamic games; linear feedback saddle-point solutions;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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