Journal of Mathematical Sciences

, Volume 147, Issue 2, pp 6639–6643 | Cite as

On some problems in geometric game theory

  • L. Ju. Blazhennova-Mikulich


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 ℝ n , (2) a closed interval, (3) a polyhedral, and the strategy set of the other player is an arbitrary convex set.


Saddle Point Closed Interval Closed Ball Convex Polyhedron Linear Dynamic System 


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  1. 1.
    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).Google Scholar
  2. 2.
    L. A. Petrosian, N. A. Zenkevich, and E. A. Semina, Game Theory [in Russian], Vysshaja Shkola, Knizhny dom “Universitet,” Moscow (1998), pp. 66–68.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • L. Ju. Blazhennova-Mikulich
    • 1
  1. 1.Moscow State UniversityRussia

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