# Stability in Repeated Matching Markets

arXiv: https://arxiv.org/abs/2007.03794 · HTML: https://mlsanity.com/paper/2007.03794/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Learn to Match with No Regret: Reinforcement Learning in Markov Matching Markets](https://mlsanity.com/paper/2203.03684/) (2022)
- [Resource Sharing Through Multi-Round Matchings](https://mlsanity.com/paper/2211.17199/) (2022)

## Abstract (arXiv)

This paper develops a framework for repeated matching markets. The model departs from the Gale-Shapley matching model by having a fixed set of long-lived hospitals match with a new generation of short-lived residents in every period. I show that there are two kinds of hospitals in this repeated environment: some hospitals can be motivated dynamically to voluntarily reduce their hiring capacity, potentially making more residents available to rural hospitals; the others, however, are untouchable even with repeated interaction and must obtain the same match as they do in a static matching. In large matching markets with correlated preferences, at most a vanishingly small fraction of the hospitals are untouchable. The vast majority of hospitals can be motivated using dynamic incentives.