Serial dictatorship is a simple mechanism for coordinating agents in solving combinatorial optimization problems according to their preferences. The most representative such problem is one-sided matching, in which a set of n agents have values for a set of n items, and the objective is to compute a matching of the agents to the items of maximum total value (a.k.a., social welfare). Following the recent framework of Caragiannis and Rathi [10], we consider a model in which the agent-item values are not available upfront but become known by querying agent sequences. In particular, when the agents are asked to act in a sequence, they respond by picking their favorite item that has not been picked by agents who acted before and reveal their value for it. Can we compute an agent sequence that induces a social welfare-optimal matching? We answer this question affirmatively and present an algorithm that uses polynomial number (n^5) of queries. This solves the main open problem stated by Caragiannis and Rathi [CR23]. Our analysis uses a potential function argument that measures progress towards learning the underlying edge-weight information. Furthermore, the algorithm has a truthful implementation by adapting the paradigm of VCG payments.

翻译：串行独裁是一种根据智能体偏好协调其解决组合优化问题的简单机制。最具代表性的此类问题是单边匹配问题，其中n个智能体对n个项目具有估值，目标是计算智能体与项目的匹配以最大化总价值（即社会福利）。遵循Caragiannis和Rathi[10]的最新研究框架，我们考虑一种模型，其中智能体-项目估值并非预先已知，而是通过查询智能体序列逐步获取。具体而言，当要求智能体按序列行动时，每个智能体会选择在其之前行动的智能体未选取的项目中最偏好的项目，并披露对该项目的估值。我们能否计算出能诱导社会福利最优匹配的智能体序列？我们对此问题给出肯定回答，并提出一种使用多项式数量（n^5）查询的算法。这解决了Caragiannis和Rathi[CR23]提出的主要开放性问题。我们的分析采用势函数论证来度量学习底层边权重信息的进展程度。此外，通过适配VCG支付范式，该算法可实现真实激励兼容的实施。