TL;DR
This paper introduces a new concept of concavity in many-to-one matching markets, establishing conditions for the existence of stable matchings and providing a class of such markets, using Scarf's algorithm.
Contribution
It defines concavity in two-sided matching markets, proves stable matchings exist under this condition, and offers a constructive method using Scarf's algorithm.
Findings
Stable matchings exist in concave markets.
A class of concave markets is characterized.
Scarf's algorithm is used to find stable matchings.
Abstract
We propose a notion of concavity in two-sided many-to-one matching, which is an analogue to the balancedness condition in cooperative games. A stable matching exists when the market is concave. We provide a class of concave markets. In the proof of the existence theorem, we use Scarf's algorithm to find a stable schedule matching, which is of independent interest.
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Taxonomy
TopicsGame Theory and Voting Systems · Game Theory and Applications · Economic theories and models