Coalitions naturally exist in many real-world systems involving multiple decision makers such as ridesharing, security, and online ad auctions, but the coalition structure among the agents is often unknown. We propose and study an important yet previously overseen problem -- Coalition Structure Learning (CSL), where we aim to carefully design a series of games for the agents and infer the underlying coalition structure by observing their interactions in those games. We establish a lower bound on the sample complexity -- defined as the number of games needed to learn the structure -- of any algorithms for CSL and propose the Iterative Grouping (IG) algorithm for designing normal-form games to achieve the lower bound. We show that IG can be extended to other succinct games such as congestion games and graphical games. Moreover, we solve CSL in a more restrictive and practical setting: auctions. We show a variant of IG to solve CSL in the auction setting even if we cannot design the bidder valuations. Finally, we conduct experiments to evaluate IG in the auction setting and the results align with our theoretical analysis.

翻译：联盟在涉及多个决策者的现实系统中自然存在，例如拼车、安全和在线广告拍卖，但智能体之间的联盟结构往往是未知的。我们提出并研究了一个重要但此前被忽视的问题——联盟结构学习（Coalition Structure Learning, CSL），其目标是为智能体精心设计一系列博弈，并通过观察它们在博弈中的交互来推断潜在的联盟结构。我们建立了任何CSL算法所需样本复杂度（定义为学习结构所需的博弈数量）的下界，并提出了迭代分组（Iterative Grouping, IG）算法用于设计正规型博弈以实现该下界。我们证明IG可以扩展到其他简洁博弈，如拥塞博弈和图博弈。此外，我们在更具限制性和实用性的场景——拍卖中——解决了CSL问题。即使无法设计竞拍者估值，我们也展示了在拍卖场景中解决CSL的IG变体。最后，我们通过实验评估了IG在拍卖场景中的性能，实验结果与理论分析一致。