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Parameter Analysis Of A Zero-Sum Differential Game Approximating A Nonzero-Sum Game

Author

Listed:
  • ARIK MELIKYAN

    (Institute for Problems in Mechanics, Russian Academy of Sciences, Vernadsky Ave., 101-1, 119526 Moscow, Russia)

  • GEERT JAN OLSDER

    (Faculty of Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands)

  • ANDREI AKHMETZHANOV

    (Institute for Problems in Mechanics, Russian Academy of Sciences, Vernadsky Ave., 101-1, 119526 Moscow, Russia)

Abstract

In this paper we consider a zero-sum differential game in feedback setting with one state coordinate and finite time horizon. The problem is characterized by two parameters. This game arises as an approximation to a nonzero-sum game. Using analytical and numerical methods we solve the HJBI equation and give the description of the optimal feedback controls for both players. These feedbacks are given in terms of switching curves and singular universal lines. We also determine the change (bifurcations) of the optimal phase portrait of the game depending upon the parameters. In conclusion, we show that for some values of the parameters the solution of the considered zero-sum game leads to the exact solution of the corresponding nonzero-sum game, and for the other values of the parameters it supplies just some approximation.

Suggested Citation

  • Arik Melikyan & Geert Jan Olsder & Andrei Akhmetzhanov, 2008. "Parameter Analysis Of A Zero-Sum Differential Game Approximating A Nonzero-Sum Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 437-459.
    • Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:n:s0219198908002035
    DOI: 10.1142/S0219198908002035
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    More about this item

    Keywords

    Differential zero-sum game; nonzero-sum game; feedback control; Subject Classification: 49N70; Subject Classification: 91A10; Subject Classification: 91A24;
    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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