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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations