ON SOME PROBLEMS IN GEOMETRIC GAME THEORY

摘要

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.