Estimating the Target Survival Probability in the Attackers–Target–Defenders Problem

The attackers–target–defenders problem is formulated and formalized as a positional zero-sum game with incomplete information. A method for estimating the target survival probability given some estimates of attackers’ dynamic capabilities is proposed, and recurrence expressions for its calculation are obtained. The corresponding numerical target survival probability estimations with optimal behavior of the players are made. The defenders in the game are assigned three different roles: the role of a false target, the target tracking role, and the attacker intercepting role. The survival probability considered as a function of the attackers–target–defenders problem parameters is analyzed. The obtained probability estimates can be used as heuristic estimates for the performance of the corresponding dynamical system. The obtained optimal strategies can be considered as heuristics for the corresponding attackers–target–defenders differential game. The optimal strategies contain orders for the players indicating their current roles. Using the Python language, we developed a software module that allows one to calculate the target survival probability based on known problem parameters.