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Strategy-proof Allocation of Indivisible Goods when Preferences are Single-peaked

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  • Mandal, Pinaki
  • Roy, Souvik

Abstract

We consider assignment problems where heterogeneous indivisible goods are to be assigned to individuals so that each individual receives at most one good. Individuals have single-peaked preferences over the goods. In this setting, first we show that there is no strategy-proof, non-bossy, Pareto efficient, and strongly pairwise reallocation-proof assignment rule on a minimally rich single-peaked domain when there are at least three individuals and at least three objects in the market. Next, we characterize all strategy-proof, Pareto efficient, top-envy-proof, non-bossy, and pairwise reallocation-proof assignment rules on a minimally rich single-peaked domain as hierarchical exchange rules. We additionally show that strategy-proofness and non-bossiness together are equivalent to group strategy-proofness on a minimally rich single-peaked domain, and every hierarchical exchange rule satisfies group-wise reallocation-proofness on a minimally rich single-peaked domain.

Suggested Citation

  • Mandal, Pinaki & Roy, Souvik, 2021. "Strategy-proof Allocation of Indivisible Goods when Preferences are Single-peaked," MPRA Paper 105320, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:105320
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    File URL: https://mpra.ub.uni-muenchen.de/105320/1/MPRA_paper_105320.pdf
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    References listed on IDEAS

    as
    1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
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    3. Mandal, Pinaki & Roy, Souvik, 2020. "Obviously Strategy-proof Implementation of Assignment Rules: A New Characterization," MPRA Paper 104044, University Library of Munich, Germany.
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    5. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
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    More about this item

    Keywords

    Assignment problem; Single-peaked preferences; Strategy-proofness; Pareto efficiency; Non-bossiness; Top-envy-proofness; Strong reallocation-proofness; Pairwise/group-wise reallocation-proofness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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