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 language | English |
|---|---|
| Article number | 14 |
| Journal | Autonomous Agents and Multi-Agent Systems |
| Volume | 36 |
| Issue number | 1 |
| DOIs | |
| State | Published - Apr 2022 |
| Externally published | Yes |
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!
| Funders | Funder number |
|---|---|
| European Cooperation in Science and Technology | EC 2016, FairDiv-15 |
| Israel Science Foundation | 712/20 |
Keywords
- Cake-cutting
- Computational geometry
- Dynamic fair division
- Land reform
- Two-dimensional resource allocation
