Differential Games

In this paper, we shall give a brief account of the main ideas in the theory of differential games. Our presentation will be limited to two player, zero sum, differential games, except for a few words regarding the situations where there are more than two players or where the game is not zero sum. To begin with, recall the game formulation when there are two players, I and II. The actions (strategies) available to I are represented by a set A = {, whereas those available to II are described by the setB = {fl}. There is specified a payoff function P: A x B -~ R, and I chooses a in A to maximize P while II chooses P3 in B to minimize P. In general, we know that the order in which the choices are made is essential, and we can only assert that