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One-Sided Matching Markets with Endowments: Equilibria and Algorithms

Authors:

Thorben Tröbst,

Vijay V. VaziraniAuthors Info & Claims

AAMAS '22: Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems

Pages 463 - 471

Published: 09 May 2022 Publication History

Abstract

The Arrow-Debreu extension of the classic Hylland-Zeckhauser scheme [27] for a one-sided matching market -- called ADHZ in this paper -- has natural applications but has instances which do not admit equilibria. By introducing approximation, we define the ε-approximate ADHZ model, and we give the following results.

(1) Existence of equilibrium under linear utility functions. We prove that the equilibrium satisfies Pareto optimality, approximate envy-freeness, and approximate weak core stability.

(2) A combinatorial polynomial-time algorithm for an ε-approximate ADHZ equilibrium for the case of dichotomous, and more generally bi-valued, utilities.

(3) An instance of ADHZ, with dichotomous utilities and a strongly connected demand graph, which does not admit an equilibrium.

(4) A rational convex program for HZ under dichotomous utilities; a combinatorial polynomial-time algorithm for this case was given in [35].

The ε-approximate ADHZ model fills a void in the space of general mechanisms for one-sided matching markets; see details in the paper.

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Cited By

Garg JTröbst TVazirani VAgmon NAn BRicci AYeoh W(2023)A Nash-Bargaining-Based Mechanism for One-Sided Matching Markets and Dichotomous UtilitiesProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3599055(2721-2723)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3599055

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One-Sided Matching Markets with Endowments: Equilibria and Algorithms

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cover image ACM Conferences

AAMAS '22: Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems

May 2022

1990 pages

ISBN:9781450392136

General Chairs:
Catherine Pelachaud
CNRS-ISIR, Sorbonne University, France
,
Matthew E. Taylor
University of Alberta, Canada
,
Program Chairs:
Piotr Faliszewski
AGH University of Science and Technology, Poland
,
Viviana Mascardi
University of Genova, Italy

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SIGAI: ACM Special Interest Group on Artificial Intelligence

Publisher

International Foundation for Autonomous Agents and Multiagent Systems

Richland, SC

Publication History

Published: 09 May 2022

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AAMAS ' 22: International Conference on Autonomous Agents and Multi-Agent Systems

May 9 - 13, 2022

Virtual Event, New Zealand

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Overall Acceptance Rate 1,155 of 5,036 submissions, 23%

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Cited By

Garg JTröbst TVazirani VAgmon NAn BRicci AYeoh W(2023)A Nash-Bargaining-Based Mechanism for One-Sided Matching Markets and Dichotomous UtilitiesProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3599055(2721-2723)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3599055

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