Bandit Learning in Decentralized Matching Markets

A fundamental question at the intersection of learning theory and game theory is as follows: how should individually rational agents act when they have to learn about the consequences of their actions in the same uncertain environment? The emerging research area of multiplayer learning-- which explores this basic question and is motivated by a broad range of modern applications, from modeling competition among firms [Mansour et al., 2018, Aridor et al., 2019] to implementing protocols for wireless networks [Liu and Zhao, 2010, Cesa-Bianchi et al., 2016, Shahrampour et al., 2017]--has been of increasing interest. A particularly salient application is the online marketplace, which can often be modeled as a two-sided matching market with uncertainty. Examples include online labor markets (Upwork and TaskRabbit for freelancing, Handy for housecleaning), online crowdsourcing platforms (Amazon Mechanical Turk), and peer-to-peer platforms (Airbnb). The multi-armed bandit is a core learning problem in which a player is faced with a choice among K actions, each of which is associated with a reward distribution, and the goal is to learn which action has the highest reward, doing so as quickly as possible so as to be able to reap rewards even while the learning process is underway. To introduce a game-theoretic aspect into the bandit problem, it is natural to place the problem into the context of a two-way matching market, where the choices faced by the players are identified with the entities on the other side of the market, and where the need to realize a matching imposes economic constraints and incentives. Such a blend of bandit learning with two-sided matching markets was introduced by Liu et al. [2020], who formulated a problem in which the players and the arms form the two sides of the market, and each side has preferences over the other side.