Many-to-many stable matching in large economies
Michael Greinecke, Karolina Vocke
TLDR
This paper develops a method to transfer stability existence results from finite to large many-to-many matching models, showing tree-stable and pairwise-stable outcomes exist.
Key contributions
- Analyzes stability in large, networked many-to-many matching markets using a distributional approach.
- Formulates outcomes as joint distributions of agent characteristics and contract choices.
- Introduces a mechanical method to transfer finite matching model existence results to large models.
- Proves the existence of tree-stable and pairwise-stable outcomes in these large economies.
Why it matters
This paper provides a crucial framework for understanding stability in large, complex matching markets where individual agents are insignificant. Its general method simplifies proving existence for various stability notions, advancing market design and economic theory.
Original 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.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.