Learning in Multi-Stage Decentralized Matching Markets
This work addresses the challenge of strategic decision-making for participants in real-world matching markets like college admissions, though it appears incremental as it builds on existing matching market frameworks.
The paper tackles the problem of learning optimal strategies in multi-stage decentralized matching markets with uncertain preferences, showing that participants can achieve higher expected payoffs through multi-stage matching compared to single-stage matching, as demonstrated via simulations and real college admissions data.
Matching markets are often organized in a multi-stage and decentralized manner. Moreover, participants in real-world matching markets often have uncertain preferences. This article develops a framework for learning optimal strategies in such settings, based on a nonparametric statistical approach and variational analysis. We propose an efficient algorithm, built upon concepts of "lower uncertainty bound" and "calibrated decentralized matching," for maximizing the participants' expected payoff. We show that there exists a welfare-versus-fairness trade-off that is characterized by the uncertainty level of acceptance. Participants will strategically act in favor of a low uncertainty level to reduce competition and increase expected payoff. We prove that participants can be better off with multi-stage matching compared to single-stage matching. We demonstrate aspects of the theoretical predictions through simulations and an experiment using real data from college admissions.