The Defense of Networked Targets in General Lotto games

Ensuring the security of networked systems is a significant problem, considering the susceptibility of modern infrastructures and technologies to adversarial interference. A central component of this problem is how defensive resources should be allocated to mitigate the severity of potential attacks on the system. In this paper, we consider this in the context of a General Lotto game, where a defender and attacker deploys resources on the nodes of a network, and the objective is to secure as many links as possible. The defender secures a link only if it out-competes the attacker on both of its associated nodes. For bipartite networks, we completely characterize equilibrium payoffs and strategies for both the defender and attacker. Surprisingly, the resulting payoffs are the same for any bipartite graph. On arbitrary network structures, we provide lower and upper bounds on the defender's max-min value. Notably, the equilibrium payoff from bipartite networks serves as the lower bound. These results suggest that more connected networks are easier to defend against attacks. We confirm these findings with simulations that compute deterministic allocation strategies on large random networks. This also highlights the importance of randomization in the equilibrium strategies.