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
Citation
CHATTERJI, Shurojit and LIU, Peng.
On the decomposability of fractional allocations. (2024). Mathematical Social Sciences. 132, 79-89.
Available at: https://ink.library.smu.edu.sg/soe_research/2785
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.mathsocsci.2024.10.002