Risk-attitude-based defense strategy considering proactive strike, preventive strike and imperfect false targets

Abstract

This paper analyzes the optimal strategies for the attacker and the defender in an attack–defense game, considering the risk attitudes of both parties. The defender moves first, allocating its limited resources to three different measures: launching a proactive strike or preventive strike, building false targets, and protecting its genuine object. It is assumed that (a) launching a proactive strike has limited effectiveness on its rival and does not expose the genuine object itself, (b) a false target might be correctly identified as false, and (c) launching a preventive strike consumes less resources than a proactive strike and might expose the genuine object. The attacker moves after observing the defender's movements, allocating its limited resources to three measures: protecting its own base from a proactive strike or preventive strike, building false bases, and attacking the defender's genuine object. For each of the defender's given strategies, the attacker chooses the attack strategy that maximizes its cumulative prospect value, which accounts for the players’ risk attitudes. Similarly, the defender maximizes its cumulative prospect value by anticipating that the attacker will always choose the strategy combination that maximizes its own cumulative prospect value. Backward induction is used to obtain the optimal defense, attack strategies, and their corresponding cumulative prospect values. Our results show that the introduction of risk attitudes leads the game to a lose-lose situation under some circumstances and benefits one party in other cases.