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On A Class Of Nash Equilibria With Memory Strategies For Nonzero-Sum Differential Games

Author

Listed:
  • JEAN MICHEL COULOMB

    (School of Mathematics, University of South Australia, The Levels, Pooraka, SA, 5095, Australia)

  • VLADIMIR GAITSGORY

    (School of Mathematics, University of South Australia, The Levels, Pooraka, SA, 5095, Australia)

Abstract

A two-player nonzero-sum differential game is considered. Given a pair of threat payoff functions, we characterise a set of pairs of acceptable feedback controls. Any such pair induces a history-dependent Nash δ-equilibrium as follows: the players agree to use the acceptable controls unless one of them deviates. If this happens, a feedback control punishment is implemented. The problem of finding a pair of "acceptable" controls is significantly simpler than the problem of finding a feedback control Nash equilibrium. Moreover, the former may have a solution in case the latter does not. In addition, if there is a feedback control Nash equilibrium, then our technique gives a subgame perfect Nash δ-equilibrium that might improve the payoff function for at least one player.

Suggested Citation

  • Jean Michel Coulomb & Vladimir Gaitsgory, 2000. "On A Class Of Nash Equilibria With Memory Strategies For Nonzero-Sum Differential Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(02n03), pages 173-192.
    • Handle: RePEc:wsi:igtrxx:v:02:y:2000:i:02n03:n:s021919890000010x
    DOI: 10.1142/S021919890000010X
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    Cited by:

    1. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.

    More about this item

    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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