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Reclaim-proof allocation of indivisible objects

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  • Ekici, Özgün

Abstract

We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.

Suggested Citation

  • Ekici, Özgün, 2013. "Reclaim-proof allocation of indivisible objects," Games and Economic Behavior, Elsevier, vol. 81(C), pages 1-10.
    • Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:1-10
    DOI: 10.1016/j.geb.2013.03.013
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    Cited by:

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    2. Jun Zhang, 2020. "Cores in discrete exchange economies with complex endowments," Papers 2005.09351, arXiv.org, revised May 2021.
    3. Ekici, Özgün, 2020. "Random mechanisms for house allocation with existing tenants," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 53-65.
    4. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    5. Fujinaka, Yuji & Wakayama, Takuma, 2018. "Endowments-swapping-proof house allocation," Games and Economic Behavior, Elsevier, vol. 111(C), pages 187-202.

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    More about this item

    Keywords

    Indivisible object allocation; House allocation with existing tenants; House allocation; Housing market; Reclaim-proof; Competitive allocation; Core;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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