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Informational uniqueness of closed-loop Nash equilibria for a class of nonstandard dynamic games

Abstract

This paper discusses an extension of the currently available theory of noncooperative dynamic games to game models whose state equations are of order higher than one. In a discrete-time framework, it first elucidates the reasons why the theory developed for first-order systems is not applicable to higher-order systems, and then presents a general procedure to obtain an informationally unique Nash equilibrium solution in the presence of random disturbances. A numerical example solved in the paper illustrates the general approach.

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References

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    Başar, T., andOlsder, G. J.,Dynamic Noncooperative Game Theory, Academic Press, New York, New York, 1982.

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    Başar, T.,On the Uniqueness of the Nash Solution in Linear-Quadratic Differential Games, International Journal of Game Theory, Vol. 5, Nos. 2/3, pp. 65–90, 1976.

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    Basar, T.,Decentralized Multicriteria Optimization of Linear Stochastic Systems, IEEE Transactions on Automatic Control, Vol. AC-23, No. 2, pp. 233–243, 1978.

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Dedicated to G. Leitmann

Research that led to this paper was supported in part by the Office of Naval Research under Contract No N00014-82-K-0469 and in part by the U.S. Air Force under Grant No. AFOSR-84-0054.

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Başar, T. Informational uniqueness of closed-loop Nash equilibria for a class of nonstandard dynamic games. J Optim Theory Appl 46, 409–419 (1985). https://doi.org/10.1007/BF00939146

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Key Words

  • Dynamic games
  • noncooperative differential games
  • Nash equilibrium solutions
  • uniqueness of equilibria
  • second-order systems
  • stochastic dynamics
  • closed-loop information patterns