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Truthful Fair Division without Free Disposal

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  • Xiaohui Bei
  • Guangda Huzhang
  • Warut Suksompong

Abstract

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

Suggested Citation

  • Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2018. "Truthful Fair Division without Free Disposal," Papers 1804.06923, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1804.06923
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    References listed on IDEAS

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    1. Haris Aziz & Anna Bogomolnaia & Hervé Moulin, 2019. "Fair Mixing: the Case of Dichotomous Preferences," Post-Print hal-03047451, HAL.
    2. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    3. Duddy, Conal, 2015. "Fair sharing under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 1-5.
    4. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    5. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    6. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
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    1. Xiaohui Bei & Xinhang Lu & Warut Suksompong, 2021. "Truthful Cake Sharing," Papers 2112.05632, arXiv.org, revised Feb 2022.

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