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：联盟结构广泛存在于涉及多个决策者的真实世界系统中，例如拼车、安全和在线广告拍卖，但代理之间的联盟结构通常是未知的。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（CSL），其目标是为代理精心设计一系列博弈，并通过观察他们在这些博弈中的交互来推断潜在的联盟结构。我们为CSL建立了任何算法在样本复杂度（定义为学习结构所需的博弈数量）上的下界，并提出了迭代分组（IG）算法用于设计正规形式博弈以实现该下界。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，我们在更严格且实用的拍卖场景中解决了CSL问题。我们展示了IG的一种变体，即使在无法设计竞拍者估值的情况下，也能在拍卖场景中解决CSL。最后，我们进行了实验以评估IG在拍卖场景中的表现，结果与我们的理论分析一致。