# Social Integration in Two-Sided Matching Markets

## TL;DR

This paper explores the effects of merging two-sided matching markets, showing that stable mechanisms limit harm to agents and can lead to expected gains, despite incompatibility with Pareto efficiency.

## Contribution

It introduces the concept of integration monotonicity and demonstrates limitations and potential benefits of market integration under stable matching mechanisms.

## Key findings

- Stable mechanisms never harm more than half of the society during integration.
- In random markets, integration yields positive expected gains for both sides.
- Integration can be beneficial despite the incompatibility with Pareto optimality.

## Abstract

When several two-sided matching markets merge into one, it is inevitable that some agents will become worse off if the matching mechanism used is stable. I formalize this observation by defining the property of integration monotonicity, which requires that every agent becomes better off after any number of matching markets merge. Integration monotonicity is also incompatible with the weaker efficiency property of Pareto optimality. Nevertheless, I obtain two possibility results. First, stable matching mechanisms never hurt more than one-half of the society after the integration of several matching markets occurs. Second, in random matching markets there are positive expected gains from integration for both sides of the market, which I quantify.