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On Level Sets With "Narrow Throats" In Linear Differential Games

Author

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  • SERGEY S. KUMKOV

    (Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str., 16, Ekaterinburg, 620219, Russia)

  • VALERY S. PATSKO

    (Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str., 16, Ekaterinburg, 620219, Russia)

  • JOSEF SHINAR

    (Faculty of Aerospace Engineering, Technion — Israel Institution of Technology, Haifa, 32000, Israel)

Abstract

Examples with zero-sum linear differential games of fixed terminal time and a convex terminal payoff function depending on two components of the phase vector are considered. Such games can have an indifferent zone with constant value function. The level set of the value function associated with the indifferent zone is called the "critical" tube. In the selected examples, the critical tube and the neighboring level sets exhibit "narrow throats". Presence of such throats requires extremely precise computations for constructing the level sets. The paper presents different forms of critical tubes with narrow throats and indicates the combinations of problem parameters that can produce them.

Suggested Citation

  • Sergey S. Kumkov & Valery S. Patsko & Josef Shinar, 2005. "On Level Sets With "Narrow Throats" In Linear Differential Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 285-311.
    • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:03:n:s0219198905000533
    DOI: 10.1142/S0219198905000533
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    More about this item

    Keywords

    Differential games; value function; level sets; numerical constructions;
    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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