Redividing the cake

Erel Segal-Halevi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division algorithms that attain various trade-off points between fairness and ownership rights, in various settings differing in the geometric constraints on the allotments: (a) no geometric constraints; (b) connectivity—the cake is a one-dimensional interval and each piece must be a contiguous interval; (c) rectangularity—the cake is a two-dimensional rectangle or rectilinear polygon and the pieces should be rectangles; (d) convexity—the cake is a two-dimensional convex polygon and the pieces should be convex. These re-division algorithms have implications on another problem: the price-of-fairness—the loss of social welfare caused by fairness requirements. Each algorithm implies an upper bound on the price-of-fairness with the respective geometric constraints.

Original languageEnglish
Article number14
JournalAutonomous Agents and Multi-Agent Systems
Volume36
Issue number1
StatePublished - Apr 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

I am currently supported by Israel Science Foundation grant 712/20. I started this work during my Ph.D. studies in Bar-Ilan university guided by Yonatan Aumann and Avinatan Hassidim [82]. I am grateful to Ioannis Caragiannis for introducing me to the Nash welfare and Nash price of fairness in the COST Summer School on Fair Division in Grenoble, 7/2015 (FairDiv-15). I benefited a lot from discussions with participants in BIU game-theory seminar, Glasgow university micro-economics seminar and Corvinus university game-theory seminar, particularly: Reuven Cohen, Herve Moulin, Yehuda Levy, Panagiotis Kanellopoulos, Laszlo Csato and Aris Filos-Ratsikas. I also received a lot of mathematical help from Chris Culter, Varun Dubey, Alex Ravsky, Swami Sarvattomananda, Zhen Lin, Sariel Har-Peled, Saeed Amiri, David Eppstein, Inuyasha Yagami, David K, [61], j_random_hacker, and WoolierThanThou. I am grateful to the anonymous reviewers of AAMAS 2016, EC 2016, SODA 2017, ESA 2017, IJCAI 2018 and the AAMAS journal for their very helpful comments. Above all, to Galya Segal-Halevi, thanks for all the cakes! I am currently supported by Israel Science Foundation grant 712/20. I started this work during my Ph.D. studies in Bar-Ilan university guided by Yonatan Aumann and Avinatan Hassidim []. I am grateful to Ioannis Caragiannis for introducing me to the Nash welfare and Nash price of fairness in the COST Summer School on Fair Division in Grenoble, 7/2015 (FairDiv-15). I benefited a lot from discussions with participants in BIU game-theory seminar, Glasgow university micro-economics seminar and Corvinus university game-theory seminar, particularly: Reuven Cohen, Herve Moulin, Yehuda Levy, Panagiotis Kanellopoulos, Laszlo Csato and Aris Filos-Ratsikas. I also received a lot of mathematical help from Chris Culter, Varun Dubey, Alex Ravsky, Swami Sarvattomananda, Zhen Lin, Sariel Har-Peled, Saeed Amiri, David Eppstein, Inuyasha Yagami, David K, [], j_random_hacker, and WoolierThanThou. I am grateful to the anonymous reviewers of AAMAS 2016, EC 2016, SODA 2017, ESA 2017, IJCAI 2018 and the AAMAS journal for their very helpful comments. Above all, to Galya Segal-Halevi, thanks for all the cakes!

FundersFunder number
European Cooperation in Science and TechnologyEC 2016, FairDiv-15
Israel Science Foundation712/20

    Keywords

    • Cake-cutting
    • Computational geometry
    • Dynamic fair division
    • Land reform
    • Two-dimensional resource allocation

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