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Differential games

In: Game Theory

Author

Listed:
  • Leon A. Petrosjan

    (Faculty of Applied Mathematics, St. Petersburg State University, Russia)

  • Nikolay A. Zenkevich

    (Faculty of Applied Mathematics, St. Petersburg State University, Russia)

Abstract

The following sections are included:Differential zero-sum games with prescribed durationMultistage perfect-information games with an infinite number of alternativesExistence of ɛ-equilibria in differential games with prescribed durationDifferential time-optimal games of pursuitNecessary and sufficient condition for existence of optimal open-loop strategy for EvaderFundamental equationMethods of successive approximations for solving differential games of pursuitExamples of solutions to differential games of pursuitGames of pursuit with delayed information for PursuerDefinition of cooperative differential game in the characteristic function formPrinciple of dynamic stability (time-consistency)Integral optimality principlesDifferential strongly time consistent optimality principlesStrongly time consistent optimality principles for the games with discount payoffsExercises and problems

Suggested Citation

  • Leon A. Petrosjan & Nikolay A. Zenkevich, 1996. "Differential games," World Scientific Book Chapters, in: Game Theory, chapter 5, pages 267-343, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812812537_0005
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    Citations

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    Cited by:

    1. Anna Tur & Leon Petrosyan, 2021. "Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure," Mathematics, MDPI, vol. 9(7), pages 1-15, April.
    2. Ovanes Petrosian & Lihong Shi & Yin Li & Hongwei Gao, 2019. "Moving Information Horizon Approach for Dynamic Game Models," Mathematics, MDPI, vol. 7(12), pages 1-31, December.

    More about this item

    Keywords

    Strategy; Optimal Solution; Nash Equilibrium; Time-Consistency; Shapley Value; Core; Extensive Game; Mixed Strategy;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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