Competing Bandits in Decentralized Large Contextual Matching Markets

Matching markets have become increasingly relevant in a variety of modern applications, including but not limited to school admissions, organ transplantation, and job matching. Traditionally, these markets were studied under the assumption that the demand side agents (aka players or agents) and the supply side agents (aka arms) have fixed, known preferences, allowing for stable matching via the deferred acceptance algorithm like the Gale-Shapley algorithm introduced in Gale and Shapley (1962). However, in applications like crowdsourcing, online labor markets, and finance, the preferences are not given to the agents, and they must learn it over time by interacting with the environment. Modeling the matching market as multi-agent, multi-armed competitive bandits, there has been extensive work on various aspects, including coordinated centralized matching, decentralized matching, and game-theoretic analysis (see Liu et al. (2020); Basu et al. (2021); Sankararaman et al. (2021); Etesami and Srikant (2024)). In this paper, we study a large and dynamic matching market where the number of arms K is large and often exceeds the number of agents N( K).