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On some problems in geometric game theory


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).

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    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).

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  • Saddle Point
  • Closed Interval
  • Closed Ball
  • Convex Polyhedron
  • Linear Dynamic System