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On the decomposability of fractional allocations

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  • Chatterji, Shurojit
  • Liu, Peng

Abstract

A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.

Suggested Citation

  • Chatterji, Shurojit & Liu, Peng, 2024. "On the decomposability of fractional allocations," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 79-89.
    • Handle: RePEc:eee:matsoc:v:132:y:2024:i:c:p:79-89
    DOI: 10.1016/j.mathsocsci.2024.10.002
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    References listed on IDEAS

    as
    1. Chatterji, Shurojit & Liu, Peng, 2020. "Random assignments of bundles," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 15-30.
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    More about this item

    Keywords

    Indivisibility; Fractional allocation; Decomposability; Maximum flow;
    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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