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Reduced-Form Allocations for Multiple Indivisible Objects under Constraints

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  • Xu Lang
  • Zaifu Yang

Abstract

We examine the implementation of reduced-form allocation rules that assign multiple indivisible objects to many agents, with incomplete information and distributional constraints across objects and agents. To obtain implementability results, we adopt a lift-and-project approach, which reduces the problem to a problem of enumerating finite generators of a projection cone. We study geometric and combinatorial properties of the projection cone and provide a total unimodularity condition that leads to several characterization results including those on hierarchies and bihierarchies. Our results have applications in matching markets with constraints where agents may have ordinal or cardinal preferences.

Suggested Citation

  • Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 21/04, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:21/04
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Debasis Mishra & Xu Lang, 2022. "Symmetric reduced form voting," Discussion Papers 22-03, Indian Statistical Institute, Delhi.
    2. Lang, Xu & Mishra, Debasis, 2024. "Symmetric reduced form voting," Theoretical Economics, Econometric Society, vol. 19(2), May.
    3. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    4. Xu Lang & Debasis Mishra, 2022. "Symmetric reduced form voting," Papers 2207.09253, arXiv.org, revised Apr 2023.
    5. Xu Lang & Zaifu Yang, 2023. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 23/02, Department of Economics, University of York.

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    More about this item

    Keywords

    Implementation; Reduced-form rules; Indivisible goods; Distributional constraints; Total unimodularity; Incomplete information.;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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