A note on the characterization of stable matchings for general preferences: a fixed point approach

Shravan Luckraz

doi:10.24193/fpt-ro.2025.1.13

A note on the characterization of stable matchings for general preferences: a fixed point approach

Research output: Journal Publication › Article › peer-review

Abstract

We represent the problem of the existence of a stable matching as a fixed point problem and show that a generalization of the no-odd ring condition is necessary and sufficient for the existence of a stable matching. Our result uses a generalization of the Abian's fixed point theorem.

Original language	English
Pages (from-to)	217-224
Journal	Fixed Point Theory
Volume	26
Issue number	1
DOIs	https://doi.org/10.24193/fpt-ro.2025.1.13
Publication status	Published - 1 Feb 2025

Keywords

Existence of stable matchings
roommate problem
fixed point theorem
graph theory
existence of equilibrium

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10.24193/fpt-ro.2025.1.13

https://math.ubbcluj.ro/~nodeacj/volumes/2025-No1/251-luc-22-0015-final-final.php

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title = "A note on the characterization of stable matchings for general preferences: a fixed point approach",

abstract = "We represent the problem of the existence of a stable matching as a fixed point problem and show that a generalization of the no-odd ring condition is necessary and sufficient for the existence of a stable matching. Our result uses a generalization of the Abian's fixed point theorem.",

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AB - We represent the problem of the existence of a stable matching as a fixed point problem and show that a generalization of the no-odd ring condition is necessary and sufficient for the existence of a stable matching. Our result uses a generalization of the Abian's fixed point theorem.

KW - Existence of stable matchings

KW - roommate problem

KW - fixed point theorem

KW - graph theory

KW - existence of equilibrium

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EP - 224

JO - Fixed Point Theory

JF - Fixed Point Theory

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A note on the characterization of stable matchings for general preferences: a fixed point approach

Abstract

Keywords

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