CHAPTER 9 - Other Approaches to Differential Games

Abstract

This chapter discusses other approaches to differential games. Approaches other than Isaacs' approach to differential games, have been developed which deal directly with solutions of differential games were developed. In some of these approaches, the existence of a solution of the game can be proved using only the properties of the direct parameters of the game. The geometric properties of games approach is not designed to prove the existence of solutions, but rather to find solutions of some games for which Isaacs' approach cannot, or for which that approach is very difficult to apply. Friedman's approach uses the method of δ-approximation of behavioral strategies, that is, every player makes decisions based on information on his/her own decisions and his/her opponent's in past moments of time and, in some cases, on additional information concerning the opponent's current decisions. On the other hand, Krasovsky's approach uses the idea of approximation in defining behavioral strategies and he uses the ideas from the geometric approach, for example, set of desired directions, in defining optimal strategies.