Move Over, Prisoner's Dilemma: Colonel Blotto has arrived

摘要

The Prisoner's Dilemma, zero-sum games, LQR team problems, and differential games have shaped game theory in controls for decades, but the field's most pressing adversarial challenges demand a richer framework, and its name is Colonel Blotto. Strategic adversarial constraints represent a fundamental consideration in control systems, from cybersecurity defense to infrastructure protection. Colonel Blotto games, despite their direct relevance to such applications, remain underutilized in the controls community relative to other game-theoretic approaches. This article aims to close that gap for the controls community. Indeed, theoretical advances within the last two decades have spurred a resurgence of interest and enabled their applications across several domains. In this article, we introduce the Colonel Blotto framework, survey key analytical and computational results, and demonstrate how problems spanning cybersecurity, network defense, and multi-agent systems fit naturally within this structure. Three research directions are examined in depth: interdependent contest objectives that capture networked vulnerabilities, alternate winning rules that model partial rewards and structural asymmetries, and multi-agent competitive environments involving coalition formation and strategic concessions. Taken together, these directions reveal a framework that is both practically deployable and rich enough to capture the strategic complexity inherent in adversarial resource allocation.