The housing market, also known as one-sided matching market, is a classic exchange economy model where each agent on the demand side initially owns an indivisible good (a house) and has a personal preference over all goods. The goal is to find a core-stable allocation that exhausts all mutually beneficial exchanges among subgroups of agents. While this model has been extensively studied in economics and computer science due to its broad applications, little attention has been paid to settings where preferences are unknown and must be learned through repeated interactions. In this paper, we propose a statistical learning model within the multi-player multi-armed bandit framework, where players (agents) learn their preferences over arms (goods) from stochastic rewards. We introduce the notion of \emph{core regret} for each player as the market objective. We study both centralized and decentralized approaches, proving $O(\log T / Δ^2)$ upper bounds on regret, where $T$ is the time horizon and $Δ$ is the minimum preference gap among players. For the decentralized setting, we also establish a matching lower bound, demonstrating that our algorithm is order-optimal.

翻译：住房市场，亦称单边匹配市场，是一种经典的交换经济模型。在该模型中，需求侧的每个智能体最初持有一件不可分割的商品（即房屋），并对所有商品具有个人偏好。其目标是找到一个核心稳定的分配方案，以穷尽智能体子群之间所有互利的交换。尽管该模型因其广泛的应用而在经济学和计算机科学领域得到了深入研究，但对于偏好未知且必须通过重复交互来学习的场景却鲜有关注。本文在多玩家多臂赌博机框架内提出了一种统计学习模型，其中玩家（智能体）通过随机奖励来学习其对臂（商品）的偏好。我们为每个玩家引入了作为市场目标的“核心遗憾”概念。我们研究了集中式与去中心化两种方法，证明了遗憾的$O(\log T / Δ^2)$上界，其中$T$是时间范围，$Δ$是玩家之间的最小偏好差距。对于去中心化设置，我们还建立了一个匹配的下界，证明了我们的算法是阶最优的。