Existence of value in generalized pursuit-evasion games

The presented results relate to a Generalized pursuit-evasion differential game (G1) and a differential game of fixed time duration(G2). The dynamics of both the games is governed by a system (2.1), (2.2) and the state variables X, Y have to satisfy constraints (2.3). Player I can apply any lower n-strategy[5, p. 400] and player II can apply any strategy in the Varaiya-Lin sense. The main result is the existence of a value in both the games and an optimal strategy for player II. The key assumption is condition (3.8) stating that the sets F2 (t,y) = {f2(t,y,v): v ?? V} are convex. This paper is an outgrowth of work conducted by the author [4-7]; it extends the results obtained in [4, 6].