An Engage or Retreat Differential Game with a Mobile Target

This paper examines a variation of the standard one-pursuer, one-evader, pursuit-evasion problem. In this problem, the evader is capable of inflicting a cost on the attacker during the pursuit. The attacker chooses whether to continue the engagement or abandon pursuit and retreat across a defined retreat boundary. The evader strategically manipulates the attacker’s cost function in order to encourage retreat. If the pursuer elects to retreat, the defender maneuvers in a way to escape to safety and prevent the pursuer from reengaging. The solution of the game is developed using analytic indirect methods and an illustrative solution is examined.