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:囚徒困境、零和博弈、LQR团队问题及微分博弈数十年来深刻塑造了控制领域的博弈论,但该领域最紧迫的对抗性挑战需要更丰富的理论框架——其名为博洛托上校博弈。从网络安全防御到基础设施保护,战略对抗约束是控制系统中的根本性考量。博洛托上校博弈虽与这些应用直接相关,却相较于其他博弈理论方法在控制学界仍未得到充分利用。本文旨在为控制学界弥合这一鸿沟。事实上,近二十年的理论突破已重新激发学界兴趣,并使其在多个领域得到应用。本文介绍博洛托上校框架,综述关键分析与计算成果,并展示网络安全、网络防御及多智能体系统等领域的问题如何自然契合该框架。我们重点探讨三个研究方向:捕捉网络脆弱性的相互依存对抗目标、建模部分收益与结构不对称性的替代胜利规则、以及涉及联盟构建与战略妥协的多智能体竞争环境。综合来看,这些方向揭示了一个既具实践部署能力,又能充分捕捉对抗性资源分配中固有战略复杂性的理论框架。