A formulation and analysis of combat games
Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games.