Optimal preventive strike strategy vs. optimal attack strategy in a defense-attack game

This paper analyzes an attack-defense game between one defender and one attacker. Among, the defender moves first and allocates its resources to three different methods: employing a preventive strike, founding false targets, and protecting its genuine object. The preventive strike may expose the genuine object, and different from previous literature, a false target may also be detected to be false. The attacker, observing the actions taken by the defender and allocating its resources to three methods: protecting its own base from the preventive strike, founding false bases, and attacking the defender's genuine object. Similarly, a false base may be correctly identified. Different from previous methods in evaluating the potential outcome, for each of the defender's given strategies, the attacker tries to maximize its cumulative prospect value considering different possible outcomes. Similarly, the defender maximizes its cumulative prospect value, assuming that the attacker chooses the strategy to maximize the attacker's cumulative prospect value. Numerical examples are presented to illustrate the optimal number of bases to attack by preventive strike, and the optimal number of targets to attack by attacker

Optimal defence-attack strategies between one defender and two attackers

This paper analyses the optimal strategies for one defender and two attackers in a defence-attack game, where a) the defender allocates its resource into defending against and attacking the two attackers, and b) the two attackers, after observing the action of the defender, allocate their resources into attacking and defending against the defender, on either a cooperative or non-cooperative basis. On a cooperative basis, for each of the defender’s given strategies, the two attackers work together to maximise the sum of their cumulative prospect values while anticipating the eight possible game outcomes. On a non-cooperative basis, for each of the defender’s given strategies, each attacker simultaneously yet independently tries to maximise their own cumulative prospect value. In both cases, the defender maximises its cumulative prospect value while anticipating the attackers’ actions. Backward induction is employed to obtain the optimal defence and attack strategies for all scenarios. Numerical examples are performed to illustrate the applications of the strategies. In general, we find two opposing effects considering the attackers’ strategies and analyse the alteration of strategies for the participants under two different risk preferences: risk-averse and risk seeking. The reasons for the alteration are also performed to illustrate the practical applications

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

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