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Reallocation Mechanisms Under Distributional Constraints in the Full Preference Domain

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Web and Internet Economics (WINE 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14413))

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Abstract

We study the problem of reallocating indivisible goods among a set of agents in one-sided matching market, where the feasible set for each good is subject to an associated distributional matroid or M-convex constraint. Agents’ preferences are allowed to have ties and not all the agents have initial endowments. We present feasible, Pareto optimal, strategy-proof mechanisms for the problems with matroid or M-convex constraints. Strategy-proofness is proved based on new structural properties over first choice graphs, which should be of independent interest. These mechanisms strictly generalize the best-known mechanism for non-strict preferences [21] with all desired properties carried over.

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Notes

  1. 1.

    In fact, in the following paragraph, the edge may have a direction from t to s, i.e., the directed edge (t, s) when referring to the first choice graph or indifference graphs. However, we will use its undirected version when we refer to Proposition 1 2 3 without causing any confusion.

  2. 2.

    One may argue that this problem can be transferred to the classical matching market by asking students to report full preference lists over all rooms instead of dormitories. However, it is not realistic in real-life applications to ask the students to report such lists over numerous rooms. See more discussion in [2, 7].

  3. 3.

    the number of copies is infinite when the constraint is matroid, and finite when the constraint is M-convex.

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Acknowledgments

This work was supported by the National Key Research and Development Program of China (2022YFF0902005). Jianwei Yin was supported by the National Science Fund for Distinguished Young Scholars (No. 61825205). Xiaoye Miao was supported by the National Natural Science Foundation of China under Grant No. 62372404, the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scholars under Grant No. LR21F020005, and the Fundamental Research Funds for the Central Universities under Grant No. 2021FZZX001-25. Jinshan Zhang was supported by the Key Research and Development Jianbing Program of Zhejiang Province (2023C01002), Hangzhou Major Project and Development Program (2022AIZD0140) and Yongjiang Talent Introduction Programm (2022A-236-G). We are also grateful for the valuable comments from the anonymous reviewers.

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Authors and Affiliations

  1. School of Software Technology, Zhejiang University, Ningbo, China

    Jinshan Zhang & Jianwei Yin

  2. Center for Data Science, Zhejiang University, Hangzhou, China

    Xiaoye Miao

  3. Databricks Inc., San Francisco, CA, USA

    Bo Tang

Authors
  1. Jinshan Zhang
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  2. Bo Tang
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  4. Jianwei Yin
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Correspondence to Xiaoye Miao .

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Editors and Affiliations

  1. Department of Industrial and Enterprise Systems Engineering, University of Illinois System, Urbana, IL, USA

    Jugal Garg

  2. Institute of Mathematics, Technische Universität Berlin, Berlin, Berlin, Germany

    Max Klimm

  3. Center on Frontiers of Computing Studies, Peking University, Beijing, Beijing, China

    Yuqing Kong

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Zhang, J., Tang, B., Miao, X., Yin, J. (2024). Reallocation Mechanisms Under Distributional Constraints in the Full Preference Domain. In: Garg, J., Klimm, M., Kong, Y. (eds) Web and Internet Economics. WINE 2023. Lecture Notes in Computer Science, vol 14413. Springer, Cham. https://doi.org/10.1007/978-3-031-48974-7_37

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  • DOI: https://doi.org/10.1007/978-3-031-48974-7_37

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-48974-7

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