# Learning in Multi-Stage Decentralized Matching Markets

arXiv: https://arxiv.org/abs/2102.06988 · HTML: https://mlsanity.com/paper/2102.06988/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 13 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [Competing Bandits in Matching Markets](https://mlsanity.com/paper/1906.05363/) (2019)
- [Bandit Learning in Decentralized Matching Markets](https://mlsanity.com/paper/2012.07348/) (2020)
- [Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation](https://mlsanity.com/paper/2005.14122/) (2020)
- [Learning Strategies in Decentralized Matching Markets under Uncertain Preferences](https://mlsanity.com/paper/2011.00159/) (2020)

## Built on by (most cited first, 12 of 12)

- [Player-optimal Stable Regret for Bandit Learning in Matching Markets](https://mlsanity.com/paper/2307.10890/) (2023)
- [Deep Learning for Two-Sided Matching](https://mlsanity.com/paper/2107.03427/) (2021)
- [Thompson Sampling for Bandit Learning in Matching Markets](https://mlsanity.com/paper/2204.12048/) (2022)
- [Incentive-Aware Recommender Systems in Two-Sided Markets](https://mlsanity.com/paper/2211.15381/) (2022)
- [Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints](https://mlsanity.com/paper/2301.10230/) (2023)
- [Competing Bandits in Time Varying Matching Markets](https://mlsanity.com/paper/2210.11692/) (2022)
- [Online Auction Design Using Distribution-Free Uncertainty Quantification with Applications to E-Commerce](https://mlsanity.com/paper/2405.07038/) (2024)
- [Long-Term Fairness in Sequential Multi-Agent Selection with Positive Reinforcement](https://mlsanity.com/paper/2407.07350/) (2024)
- [Learn then Decide: A Learning Approach for Designing Data Marketplaces](https://mlsanity.com/paper/2503.10773/) (2025)
- [Optimal Analysis for Bandit Learning in Matching Markets with Serial Dictatorship](https://mlsanity.com/paper/2512.06758/) (2025)
- [Double Auctions with Two-sided Bandit Feedback](https://mlsanity.com/paper/2208.06536/) (2022)
- [An ODE Model for Dynamic Matching in Heterogeneous Networks](https://mlsanity.com/paper/2302.09757/) (2023)

## Abstract (arXiv)

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.