Stability in Repeated Matching Markets

TL;DR

This paper introduces a framework for repeated matching markets where hospitals and residents interact over time, revealing that most hospitals can be incentivized to reduce capacity, unlike a small subset that remain static.

Contribution

It develops a dynamic model of repeated matching markets showing how incentives can influence hospital capacity decisions over time.

Findings

Most hospitals can be incentivized to reduce capacity in large markets.

A small fraction of hospitals remain untouchable and static.

Dynamic incentives can improve matching efficiency.

Abstract

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.