Abstract
Several problems of dynamic systems control can be reduced to geometric games. The problem of stabilization is an example. In this paper, the criteria of a saddle point in a geometric game is proved under more general conditions than earlier. Algorithms for finding a saddle point are given in cases where the strategy set of one of the players is (1) a ball in ℝn, (2) a closed interval, (3) a polyhedral, and the strategy set of the other player is an arbitrary convex set.
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V. V. Alexandrov, L. Ju. Blazhennova-Mikulich, I. M. Gutieres-Arias, and S. S. Lemak, “Mild testing of the stabilization precision and saddle points in geometric games,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 1, 43–50 (2005).
L. A. Petrosian, N. A. Zenkevich, and E. A. Semina, Game Theory [in Russian], Vysshaja Shkola, Knizhny dom “Universitet,” Moscow (1998), pp. 66–68.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 131–137, 2005.
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Blazhennova-Mikulich, L.J. On some problems in geometric game theory. J Math Sci 147, 6639–6643 (2007). https://doi.org/10.1007/s10958-007-0500-z
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DOI: https://doi.org/10.1007/s10958-007-0500-z