DISCRETE OPERATIONAL CALCULUS IN DELAYED STOCHASTIC GAMES

This article deals with classes of antagonistic games with two players. A game is specified in terms of two “hostile” stochastic processes representing mutual attacks upon random times that exert casualties of random magnitudes. The game ends when one of the players is defeated, that is, when the amounts of casualties to the players cross respective tolerance thresholds. We target the first passage time τ_ρ of the defeat and the amount of casualties to either player upon τρ. Here we validate our claim of analytic tractability in formulas obtained in [1] under various transforms.