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Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness

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  • Warut Suksompong
  • Nicholas Teh

Abstract

We study the problem of fairly allocating indivisible goods to agents with weights corresponding to their entitlements. Previous work has shown that, when agents have binary additive valuations, the maximum weighted Nash welfare rule is resource-, population-, and weight-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. We generalize these results to the class of weighted additive welfarist rules with concave functions and agents with matroid-rank (also known as binary submodular) valuations.

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  • Warut Suksompong & Nicholas Teh, 2023. "Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness," Papers 2303.14454, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2303.14454
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    References listed on IDEAS

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    1. Camacho, Franklin & Fonseca-Delgado, Rigoberto & Pino Pérez, Ramón & Tapia, Guido, 2023. "Generalized binary utility functions and fair allocations," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 50-60.
    2. Luisa Montanari & Ulrike Schmidt-Kraepelin & Warut Suksompong & Nicholas Teh, 2022. "Weighted Envy-Freeness for Submodular Valuations," Papers 2209.06437, arXiv.org.
    3. Mithun Chakraborty & Ulrike Schmidt-Kraepelin & Warut Suksompong, 2021. "Picking Sequences and Monotonicity in Weighted Fair Division," Papers 2104.14347, arXiv.org, revised Aug 2021.
    4. Suksompong, Warut & Teh, Nicholas, 2022. "On maximum weighted Nash welfare for binary valuations," Mathematical Social Sciences, Elsevier, vol. 117(C), pages 101-108.
    5. Warut Suksompong & Nicholas Teh, 2022. "On Maximum Weighted Nash Welfare for Binary Valuations," Papers 2204.03803, arXiv.org, revised Apr 2022.
    6. Mithun Chakraborty & Ayumi Igarashi & Warut Suksompong & Yair Zick, 2019. "Weighted Envy-Freeness in Indivisible Item Allocation," Papers 1909.10502, arXiv.org, revised Mar 2021.
    7. Sheung Man Yuen & Warut Suksompong, 2023. "Extending the Characterization of Maximum Nash Welfare," Papers 2301.03798, arXiv.org, revised Feb 2023.
    8. Yuen, Sheung Man & Suksompong, Warut, 2023. "Extending the characterization of maximum Nash welfare," Economics Letters, Elsevier, vol. 224(C).
    9. Suksompong, Warut, 2023. "A characterization of maximum Nash welfare for indivisible goods," Economics Letters, Elsevier, vol. 222(C).
    10. Jonathan Scarlett & Nicholas Teh & Yair Zick, 2023. "For One and All: Individual and Group Fairness in the Allocation of Indivisible Goods," Papers 2302.06958, arXiv.org.
    11. Moshe Babaioff & Noam Nisan & Inbal Talgam-Cohen, 2021. "Competitive Equilibrium with Indivisible Goods and Generic Budgets," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 382-403, February.
    12. Bettina Klaus & Eiichi Miyagawa, 2002. "Strategy-proofness, solidarity, and consistency for multiple assignment problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 421-435.
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