Encouraging attacker retreat through defender cooperation

This paper is motivated by a desire to develop analytic formulations for adversarial interactions between an attacker and a defensive team. We analyze a multi-stage, two-player game in which one player represents an attacker with superior dynamic characteristics and the other player represents a team consisting of a mobile, high-value target and N protective agents. At the start of the game, the attacker must decide whether to engage the target or retreat. The defending team must then decide whether to maximize or minimize the attacker´s cost in response. These decisions are referred to as the players´ intent. After each side has selected an intent, a differential pursuit-evasion game is played in which the value represents the integral cost to the attacker. Within the differential game, the terminal conditions and the players´ optimal control strategies are dictated by the previous intent selections. We obtain the optimal intent strategies in terms of the differential game values and relevant bonus and penalty values. We solve the differential games by developing the optimality conditions for the equilibrium control strategies. We show that for certain conditions, the defenders should cooperate with the attacker so that retreat becomes the most attractive option; thereby, fulfilling the defensive goal of protecting the high-value target.