FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 8, PAGES 131-137

On some problems in geometric games theory

L. Ju. Blazhennova-Mikulich

Abstract

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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 of 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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