A Game with Program Control and Variable Terminal Moment

Contents Introduction 1 1 A Scalar Game Problem 2 2 Continuous Strategies 3 3 Discontinuous Strategies -- iii -- About the Author S. A. Brykalov Department of Dynamical Systems Institute of Mathematics and Mechanics Ekaterinburg, Russia --1-- A Game with Program Control and Variable Terminal Moment S.A. Brykalov * (brykalov@imm.uran.ru) In the theory of positional di#erential games, it is well known that continuous strategies, generally speaking, do not provide the best possible result. In the present paper, a simple example is given that shows that a similar property holds for conflict control systems in which one of the two players chooses a program control, and the other one chooses the moment of termination of the game, in which the payo# is calculated. The payo# functional depends on the phase state at this time moment. It is shown that in this control system no rule for choosing the te