On the decomposability of fractional allocations

Shurojit Chatterji and Peng Liu

Mathematical Social Sciences, 2024, vol. 132, issue C, 79-89

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.

Keywords: Indivisibility; Fractional allocation; Decomposability; Maximum flow (search for similar items in EconPapers)
JEL-codes: C78 D82 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:132:y:2024:i:c:p:79-89

DOI: 10.1016/j.mathsocsci.2024.10.002

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