We consider the Coalition Structure Learning (CSL) problem in multi-agent systems, motivated by the existence of coalitions in many real-world systems, e.g., trading platforms and auction systems. In this problem, there is a hidden coalition structure within a set of $n$ agents, which affects the behavior of the agents in games. Our goal is to actively design a sequence of games for the agents to play, such that observations in these games can be used to learn the hidden coalition structure. In particular, we consider the setting where in each round, we design and present a game together with a strategy profile to the agents, and receive a multiple-bit observation -- for each agent, we observe whether or not they would like to deviate from the specified strategy. We show that we can learn the coalition structure in $O(\log n)$ rounds if we are allowed to design any normal-form game, matching the information-theoretical lower bound. For practicality, we extend the result to settings where we can only choose games of a specific format, and design algorithms to learn the coalition structure in these settings. For most settings, our complexity matches the theoretical lower bound up to a constant factor.

翻译：本文研究多智能体系统中的联盟结构学习问题，其现实背景源于交易平台与拍卖系统等实际场景中普遍存在的联盟现象。该问题假设在n个智能体间存在隐藏的联盟结构，该结构将影响智能体在博弈中的行为表现。我们的研究目标是通过主动设计一系列博弈序列供智能体参与，利用这些博弈中的观察数据来推断隐藏的联盟结构。具体而言，我们考虑以下设定：在每轮博弈中，我们向智能体展示设计的博弈及其策略组合，并接收多比特观察结果——针对每个智能体，我们观测其是否倾向于偏离指定策略。理论分析表明，若允许设计任意标准形式的博弈，我们能够在O(log n)轮内完成联盟结构学习，该结果达到了信息论下界。为提升实用性，我们将该结论推广至仅能选择特定格式博弈的场景，并设计了相应场景下的联盟结构学习算法。在多数设定下，我们的算法复杂度在常数因子范围内达到了理论下界。