Numerical Solution of Three Stochastic Differential Games

摘要

Stochastic versions of three differential games, namely: the blocking game, the game of patrolling a channel, and the collision avoidance game, are considered. The common factor of these differential games is that all three of them are modelled by the same group of stochastic differential equations. In each of the games, sufficient conditions on optimal strategies in the case of complete observation, and sufficient conditions on weak optimal strategies in the case of partial observations are derived. In the cases of complete observation, optimal strategies are computed for a variety of cases. In the cases of partial observation, procedures for computing weak suboptimal strategies are suggested, and these are computed for a variety of examples.