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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Başar, T., andOlsder, G. J.,Dynamic Noncooperative Game Theory, Academic Press, New York, New York, 1982.
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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
- Dynamic games
- noncooperative differential games
- Nash equilibrium solutions
- uniqueness of equilibria
- second-order systems
- stochastic dynamics
- closed-loop information patterns