Antagonistic games with interval parameters. (English. Russian original) Zbl 0964.91005

Cybern. Syst. Anal. 35, No. 4, 644-652 (1999); translation from Kibern. Sist. Anal. 1999, No. 4, 149-160 (1999).
Summary: Antagonistic (matrix) games with payoff matrices given to within an interval are considered. The necessary and sufficient conditions of existence of solutions of such games are established. It is shown that the basic theorem of the von Neumann theory is not valid for such games. The method of solution of a interval game by reducing it to two boundary exact games is proposed.


91A05 2-person games
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[1] Von Neumann, J.; Morgenstern, O., Theory of Games and Economic Behavior (1970), Moscow: Nauka, Moscow · Zbl 0205.23401
[2] Rozen, V. V., Mixed extensions of games with ordered sums, Zh. Vychisl. Mat. Mat. Fiz., 16, No. 6, 1436-1450 (1976) · Zbl 0392.90092
[3] Alefeld, G.; Herzberger, J., Introduction to Interval Computations (1987), Moscow: Mir, Moscow
[4] V. I. Levin, “Discrete optimization under condition of interval uncertainty,” Avtomat. Telemekh., No. 7, 97-106 (1992).
[5] V. I. Levin, “Nondeterministic infinite-valued logic and its application,” in: Proc. 12th Symp. Logical Control Using a Computer [in Russian], Moscow (1989), pp. 20-26.
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