THE CUBIC ALGORITHM FOR GLOBAL GAMES WITH APPLICATION TO PURSUIT-EVASION GAMES

New algorithms for solution of nonconvex global games defined over a c ube are presented. Application to differential games and to pursuit-ev asion games is considered, and extension is made for games over genera l compact and robust sets defined by constraints that may depend on ti me and on state variables. The methods are deterministic and monotonic ally set-convergent to deliver, in the limit, the unique exact full gl obally optimal minimax and maximin solutions for both players, or the entire global saddle set, if it exists. A stopping rule is provided fo r determining approximate solutions with a given precision in a finite number of iterations. A modification is considered to play on mistake s of the opponent. On-line replacement of cost functionals is possible in the course of iterations, according to changing interests of the p layers. No separability nor convexity-concavity assumptions are impose d on the cost functional, and variational methods are not used. The id eas are illustrated by examples and application is made to determining the globally optimal closed-loop strategies for the ship-torpedo coll ision-avoidance differential game with manoeuvrability constraints.