research-article

The Complexity of Fairness Through Equilibrium

Authors:

Abraham Othman,

Christos Papadimitriou,

Aviad RubinsteinAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 4, Issue 4

Article No.: 20, Pages 1 - 19

https://doi.org/10.1145/2956583

Published: 16 August 2016 Publication History

Abstract

Competitive equilibrium from equal incomes (CEEI) is a well-known fair allocation mechanism with desirable fairness and efficiency properties; however, with indivisible resources, a CEEI may not exist [Foley 1967; Varian 1974; Thomson and Varian 1985]. It was shown in Budish [2011] that in the case of indivisible resources, there is always an allocation, called A-CEEI, that is approximately fair, approximately truthful, and approximately efficient for some favorable approximation parameters. A heuristic search that attempts to find this approximation is used in practice to assign business school students to courses. In this article, we show that finding the A-CEEI allocation guaranteed to exist by Budish’s theorem is PPAD-complete. We further show that finding an approximate equilibrium with better approximation guarantees is even harder: NP-complete.

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Cited By

Brânzei SSandomirskiy F(2024)Algorithms for Competitive Division of ChoresMathematics of Operations Research10.1287/moor.2023.136149:1(398-429)Online publication date: Feb-2024
https://doi.org/10.1287/moor.2023.1361
Chen XKroer CKumar R(2024)The Complexity of Pacing for Second-Price AuctionsMathematics of Operations Research10.1287/moor.2022.000949:4(2109-2135)Online publication date: Nov-2024
https://doi.org/10.1287/moor.2022.0009
Gao RRoghani MRubinstein ASaberi A(2024)Hardness of Approximate Sperner and Applications to Envy-Free Cake Cutting2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00085(1294-1331)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00085
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Index Terms

The Complexity of Fairness Through Equilibrium
1. Applied computing
  1. Law, social and behavioral sciences

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 4, Issue 4

Special Issue on EC'14

August 2016

147 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/2983294

Editors:
Vincent Conitzer
Duke University
,
Preston McAfee
Microsoft

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Copyright © 2016 ACM.

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Association for Computing Machinery

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Publication History

Published: 16 August 2016

Accepted: 01 November 2015

Revised: 01 June 2015

Received: 01 December 2014

Published in TEAC Volume 4, Issue 4

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Cited By

Brânzei SSandomirskiy F(2024)Algorithms for Competitive Division of ChoresMathematics of Operations Research10.1287/moor.2023.136149:1(398-429)Online publication date: Feb-2024
https://doi.org/10.1287/moor.2023.1361
Chen XKroer CKumar R(2024)The Complexity of Pacing for Second-Price AuctionsMathematics of Operations Research10.1287/moor.2022.000949:4(2109-2135)Online publication date: Nov-2024
https://doi.org/10.1287/moor.2022.0009
Gao RRoghani MRubinstein ASaberi A(2024)Hardness of Approximate Sperner and Applications to Envy-Free Cake Cutting2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00085(1294-1331)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00085
Nan TGao YKroer CWilliams BChen YNeville J(2023)Fast and interpretable dynamics for fisher markets via block-coordinate updatesProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i5.25723(5832-5840)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i5.25723
Budish EGao ROthman ARubinstein AZhang QLeyton-Brown KSamuelson LHartline J(2023)Practical algorithms and experimentally validated incentives for equilibrium-based fair division (A-CEEI)Proceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597809(337-368)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597809
Chen XPeng BSaha BServedio R(2023)Complexity of Equilibria in First-Price Auctions under General Tie-Breaking RulesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585195(698-709)Online publication date: 2-Jun-2023
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Papadimitriou CPeng B(2023)Public goods games in directed networksGames and Economic Behavior10.1016/j.geb.2023.02.002139(161-179)Online publication date: May-2023
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Brânzei SNisan NKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)The query complexity of cake cuttingProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3603017(37905-37919)Online publication date: 28-Nov-2022
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Präntare FOsipov GEriksson LPelachaud CTaylor MFaliszewski PMascardi V(2022)Concise Representations and Complexity of Combinatorial Assignment ProblemsProceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems10.5555/3535850.3536086(1714-1716)Online publication date: 9-May-2022
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Grishutin AMusatov D(2022)Discrete Versions of the KKM Lemma and Their PPAD-CompletenessComputer Science – Theory and Applications10.1007/978-3-031-09574-0_11(170-189)Online publication date: 29-Jun-2022
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