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.
翻译:[translated abstract in Chinese]
囚徒困境、零和博弈、LQR团队问题与微分博弈在过去数十年间塑造了控制领域的博弈论研究格局,然而该领域最紧迫的对抗性挑战需要更丰富的理论框架,布拉托上校博弈应运而生。从网络安全防御到基础设施保护,战略对抗约束已成为控制系统的核心考量要素。尽管布拉托上校博弈与这些应用场景直接相关,但在控制学界其应用程度远不及其他博弈论方法。本文旨在弥合这一研究空白。事实上,近二十年的理论突破重新激发了学界对该领域的兴趣,并推动了其在多个领域的应用。本文系统介绍布拉托上校博弈框架,梳理关键解析解与计算成果,并论证网络安全、网络防御及多智能体系统等问题如何天然契合该框架。重点探讨三大研究方向:刻画网络脆弱性的关联竞争目标、建模部分收益与结构非对称性的替代胜负规则,以及涉及联盟形成与战略让步的多智能体竞争环境。综合研究表明,该框架兼具实践部署价值,能够充分捕捉对抗性资源分配中固有的战略复杂性。