IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v06y2004i01ns0219198904000137.html
   My bibliography  Save this article

Some Properties Of The Bellman–Isaacs Equation For The Games On Surfaces Of Revolution

Author

Listed:
  • ARIK MELIKYAN

    (Institute for Problems in Mechanics, Russian Academy of Sciences, Vernadsky Ave., 101-1, Moscow 117526, Russia)

Abstract

Certain geometrical properties of a dynamic game may generate a situation when in some subspaceDof the game space the game value depends only on the coordinates of one of the players. Consequently, that player has a definite optimal behavior, while the other one may exploit an arbitrary control till reaching the boundary ofD. In other words, inDone has an optimal control problem rather than a dynamic game. We show that such phenomenon takes place in pursuit-evasion games on a family of 2D surfaces of revolution, including the cones and the hyperboloids of two sheets, due to special convexity properties of the reachability sets of the players. The complete solution of the games on cones one can find in Melikyan [1998], Melikyan,et al.[1998], the games on hyperboloids are investigated in Hovakimyan and Melikyan [2000]. This paper presents new results for the latter games. In the considerations an important role happen to play the focal points, conjugate to the pursuer's positions in the variational problem on geodesic lines.

Suggested Citation

  • Arik Melikyan, 2004. "Some Properties Of The Bellman–Isaacs Equation For The Games On Surfaces Of Revolution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 171-179.
    • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000137
    DOI: 10.1142/S0219198904000137
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198904000137
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198904000137?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Pursuit–evasion game; hyperboloids; surfaces of revolution;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000137. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.