THE LINEAR QUADRATIC DYNAMIC GAME FOR DISCRETE-TIME DESCRIPTOR SYSTEMS

Hua Xu () and Hiroaki Mukaidani
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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

International Game Theory Review (IGTR), 2003, vol. 05, issue 04, 361-374

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.

Keywords: Descriptor systems; dynamic games; linear feedback saddle-point solutions (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0219198903001100

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