Networked Multi-Resource Defense Capabilities in a General Lotto Game

Abstract

Ensuring the security of complex systems involves the strategic allocation of defensive resources to prevent various types of attacks from succeeding. A defender often has multiple types of defensive assets at its disposal, where it must decide how to optimally deploy their heterogeneous capabilities across different attack types. In this paper, we formulate a multi-resource allocation problem in the form of a General Lotto game where a defender possesses various types of resources. A feature that we introduce is that their individual effectiveness against different types of attacks is characterized by a network weight matrix. In our analysis, we derive upper and lower bounds on the performance of the defender, and provide numerical evidence suggesting that they are tight. For the case of two attack types, we analytically prove that the bounds coincide, establishing an exact equilibrium characterization. We then numerically compare our proposed networked multi-resource architecture to an independent-defense benchmark from the existing literature. These results highlight fundamental and tractable structures underlying multi-attack-type defense problems.