TL;DR
This paper investigates the existence of stable matchings in firm-worker hypergraphs, showing that stability is guaranteed when the hypergraph has no nontrivial odd-length cycles, especially in specialized matching scenarios.
Contribution
It introduces a novel condition based on hypergraph cycles that ensures stable matchings in complex firm-worker matching models.
Findings
Stable matchings exist when the hypergraph has no nontrivial odd cycles.
The condition applies to matching specialized firms with specialists.
The results extend to both transferable and discrete utilities.
Abstract
A firm-worker hypergraph consists of edges in which each edge joins a firm and its possible employees. We show that a stable matching exists in both many-to-one matching with transferable utilities and discrete many-to-one matching when the firm-worker hypergraph has no nontrivial odd-length cycle. Firms' preferences satisfying this condition arise in a problem of matching specialized firms with specialists.
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Taxonomy
TopicsGame Theory and Voting Systems · Game Theory and Applications