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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 heterogeneous 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 enables us to find a general condition called total unimodularity, a well-recognized class of matrices with simple entries of −1, 0, or 1. This condition yields several new and general characterization results including those on hierarchies, bihierarchies, adjacency, and paramodularity. Our model and results extend and unify many well-known ones, cover both universal implementation and quotas-dependent implementation, and offer several new applications of practical interest.

Suggested Citation

  • Xu Lang & Zaifu Yang, 2023. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 23/02, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:23/02
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    References listed on IDEAS

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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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