IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v05y2003i02ns0219198903000878.html
   My bibliography  Save this article

Verification Theorems for Optimal Feedback Strategies in Differential Games

Author

Listed:
  • Ştefan Mirică

    (Faculty of Mathematics, University of Bucharest, Academiei 14 70109 Bucharest, Romania)

Abstract

We give complete proofs to the verification theorems announced recently by the author for the "pairs of relatively optimal feedback strategies" of an autonomous differential game. These concepts are considered to describe the possibly optimal solutions of a differential game while the corresponding value functions are used as "instruments" for proving the relative optimality and also as "auxiliary characteristics" of the differential game. The 6 verification theorems in the paper are proved under different regularity assumptions accompanied by suitable differential inequalities verified by the generalized derivatives, mainly of contingent type, of the value function.

Suggested Citation

  • Ştefan Mirică, 2003. "Verification Theorems for Optimal Feedback Strategies in Differential Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 167-189.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:02:n:s0219198903000878
    DOI: 10.1142/S0219198903000878
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198903000878
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198903000878?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

    Differential game; dynamic programming; relatively optimal feedback strategy; value function; verification theorem; Nonsmooth Analysis; monotonicity; 49N70; 49N35; 49L20; 91A23;
    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:05:y:2003:i:02:n:s0219198903000878. 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.