On the decomposability of fractional allocations

On the decomposability of fractional allocations

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 c...

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Main Authors: CHATTERJI, Shurojit, LIU, Peng
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2024
Subjects:
Indivisibility
Fractional allocation
Decomposability
Maximum flow
Economic Theory
Online Access:https://ink.library.smu.edu.sg/soe_research/2785
https://ink.library.smu.edu.sg/context/soe_research/article/3784/viewcontent/Decomposability_Fractional_Allocations_sv.pdf
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Institution: Singapore Management University
Language: English
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spelling sg-smu-ink.soe_research-37842024-12-24T02:45:29Z On the decomposability of fractional allocations CHATTERJI, Shurojit LIU, Peng 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. 2024-12-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2785 info:doi/10.1016/j.mathsocsci.2024.10.002 https://ink.library.smu.edu.sg/context/soe_research/article/3784/viewcontent/Decomposability_Fractional_Allocations_sv.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Indivisibility Fractional allocation Decomposability Maximum flow Economic Theory
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Indivisibility
Fractional allocation
Decomposability
Maximum flow
Economic Theory
spellingShingle Indivisibility
Fractional allocation
Decomposability
Maximum flow
Economic Theory
CHATTERJI, Shurojit
LIU, Peng
On the decomposability of fractional allocations
description 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.
format text
author CHATTERJI, Shurojit
LIU, Peng
author_facet CHATTERJI, Shurojit
LIU, Peng
author_sort CHATTERJI, Shurojit
title On the decomposability of fractional allocations
title_short On the decomposability of fractional allocations
title_full On the decomposability of fractional allocations
title_fullStr On the decomposability of fractional allocations
title_full_unstemmed On the decomposability of fractional allocations
title_sort on the decomposability of fractional allocations
publisher Institutional Knowledge at Singapore Management University
publishDate 2024
url https://ink.library.smu.edu.sg/soe_research/2785
https://ink.library.smu.edu.sg/context/soe_research/article/3784/viewcontent/Decomposability_Fractional_Allocations_sv.pdf
_version_ 1820027804696182784

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