Modeling arbitrary layers of continuous-level defenses in facing with strategic attackers

We propose a novel class of game-theoretic models for the optimal assignment of defensive resources in a game between a defender and an attacker. Compared to the other game-theoretic models in the literature of defense allocation problems, the novelty of our model is that we allow the defender to assign her continuous-level defensive resources to any subset (or arbitrary layers) of targets due to functional similarity or geographical proximity. We develop methods to solve for equilibrium, and illustrate our model using numerical examples. Compared to traditional models that only allow for individual target hardening, our results show that our model could significantly increase the defender's payoff, especially when the unit cost of defense is high.