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: | , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2021
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| Online Access: | https://ink.library.smu.edu.sg/soe_research/2493 https://ink.library.smu.edu.sg/context/soe_research/article/3492/viewcontent/Decomposability_.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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