Guaranteed strategies with memory for alternative pursuit

A game is called alternative if it may be terminated by the pursuer on any of two given terminal manifolds, where the payoffs of Boltza type differ only in their terminal parts. Assuming that the optimal strategies and trajectories for both corresponding games with given symmetric alternatives known, we discuss how to construct pursuit strategies that provide a guaranteed outcome in the original game. We describe a pursuit strategy with memory and a finite number of admissible updates for the targeted terminal alternative and study its guaranteed features.