Many-to-many stable matching in large economies

TL;DR

This paper develops a framework for analyzing stability in large many-to-many matching markets with complex agent characteristics, extending finite model results to large economies.

Contribution

It introduces a mechanical method to transfer existence results from finite to large matching models for various stability notions.

Findings

Tree-stable outcomes exist in large economies.

Pairwise-stable outcomes exist in large economies.

The framework handles arbitrary Polish space characteristics.

Abstract

We study stability notions for networked many-to-many matching markets with individually insignificant agents in distributional form. Outcomes are formulated as joint distributions over characteristics of agents and contract choices. Characteristics can lie in an arbitrary Polish space. We provide a mechanical method for transferring existence results for finite matching models to large matching models for many stability notions. In particular, we show that tree-stable and pairwise-stable outcomes exist.