Minimization of Fatalities in a Nuclear Attack Model

This paper considers a two-sided war game in which one side (the defender) must first deploy its defenses, consisting of both a passive defense (shelters), and an active defense (anti-missile missiles); the other side (the attacker) then decides how to aim its missiles. The defender is constrained by budget limitations, while the attacker is constrained by the number of missiles available. The payoff is in term of fatalities. The paper uses a convex duality theorem to change the min-max problem to a pure minimization problem, and obtains a solution that obeys the no-soft-spot rule. An example shows the effects of attack and budget sizes, as well as of the costs of ABM defense.