research-article

On finding an envy-free Pareto-optimal division

Authors:

J. H. Reijnierse,

J. A. M. PottersAuthors Info & Claims

Mathematical Programming, Volume 83, Issue 1-3

Pages 291 - 311

https://doi.org/10.1007/BF02680564

Published: 15 March 2023 Publication History

Abstract

This paper describes an algorithm to find an (α-)envy-free Pareto-optimal division in the case of a finite number of homogeneous infinitely divisible goods and linear utility functions. It is used to find an allocation in the classical cake division problem that is almost Pareto-optimal and α-envy-free.

References

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Brams S. and Taylor A. An envy free cake division algorithm, Mimeo, Department of Politics 1992 New York New York University

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Ford L. and Fulkerson D. Maximal flow through a network Canadian Journal of Mathematics 1956 8 399-404

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Gale D. The theory of linear economic models 1960 New York McGraw-Hill 281-287

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Knaster B. Sur le problème du partage pragmatique de H. Steinhaus Annales de la Société Polonaise de Mathematique 1946 19 228-230

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Steinhaus H. The problem of fair division Econometrica 1948 16 101-104

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Steinhaus H. Sur la division pragmatique Econometrica 1949 17 315-319

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Chakraborty MSegal-Halevi ESuksompong W(2024)Weighted Fairness Notions for Indivisible Items RevisitedACM Transactions on Economics and Computation10.1145/366579912:3(1-45)Online publication date: 6-Sep-2024
https://dl.acm.org/doi/10.1145/3665799
Rachmut BNelke SZivan RAgmon NAn BRicci AYeoh W(2023)Asynchronous Communication Aware Multi-Agent Task AllocationProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598927(2340-2342)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598927
Rachmut BNelke SZivan RElkind E(2023)Asynchronous communication aware multi-agent task allocationProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/30(262-270)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/30

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Information

Published In

cover image Mathematical Programming: Series A and B

Mathematical Programming: Series A and B Volume 83, Issue 1-3

Jan 1998

437 pages

ISSN:0025-5610

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 March 2023

Revision received: 30 October 1996

Received: 05 December 1994

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Cited By

View all

Chakraborty MSegal-Halevi ESuksompong W(2024)Weighted Fairness Notions for Indivisible Items RevisitedACM Transactions on Economics and Computation10.1145/366579912:3(1-45)Online publication date: 6-Sep-2024
https://dl.acm.org/doi/10.1145/3665799
Rachmut BNelke SZivan RAgmon NAn BRicci AYeoh W(2023)Asynchronous Communication Aware Multi-Agent Task AllocationProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598927(2340-2342)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598927
Rachmut BNelke SZivan RElkind E(2023)Asynchronous communication aware multi-agent task allocationProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/30(262-270)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/30

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Envy-free pricing in multi-item markets