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There is a heterogeneous resource that contains both good parts and bad parts, for example, a cake with some parts burnt, a land-estate with some parts heavily taxed, or a chore with some parts fun to do.
The problem of fair division
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Rental Harmony: Sperner’s Lemma in Fair Division
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A pie that can’t be cut fairly. In Dagstuhl Seminar Proceedings 07261
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Envy-free cake divisions cannot be found by finite protocols
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Envy-Free Cake-Cutting in Two Dimensions. In Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI-15)
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A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents. In FOCS 2016
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Competitive division of a mixed manna
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The Query Complexity of Cake Cutting
Simina Brânzei and Noam Nisan. 2017 · 2017
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Externalities in Cake Cutting. In Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence
Simina Brânzei, Ariel D. Procaccia, and Jie Zhang. 2013 · 2013
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Oleg R. Musin. 2014 · 2014
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Computational Fair Division
Simina Brânzei. 2015 · 2015
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Spliddit: Unleashing Fair Division Algorithms
Jonathan Goldman and Ariel D. Procaccia. 2015 · 2015
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Achieving rental harmony with a secretive roommate
Florian Frick, Kelsey Houston-Edwards, and Frédéric Meunier. 2017 · 2017
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Fair Division of Land
Erel Segal-Halevi. 2017 · 2017
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Fair and square: Cake-cutting in two dimensions
Erel Segal-Halevi, Shmuel Nitzan, Avinatan Hassidim, and Yonatan Aumann. 2017 · 2017
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Envy-free divisions of a partially burnt cake
Frédéric Meunier and Shira Zerbib. 2018 · 2018
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Fairly Dividing a Cake after Some Parts Were Burnt in the Oven. In Proceedings of AAMAS-18
Erel Segal-Halevi. 2018 · 2018
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