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.