Publication Type

Journal Article

Version

submittedVersion

Publication Date

12-2024

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

Discipline

Economic Theory

Research Areas

Economic Theory

Publication

Mathematical Social Sciences

Volume

132

First Page

79

Last Page

89

ISSN

0165-4896

Identifier

10.1016/j.mathsocsci.2024.10.002

Publisher

Elsevier

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.mathsocsci.2024.10.002

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