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On the Decomposability of Fractional Allocations

Shurojit Chatterji () and Peng Liu ()
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Shurojit Chatterji: School of Economics, Singapore Management University
Peng Liu: East China Normal University

No 3-2021, Economics and Statistics Working Papers from Singapore Management University, School of Economics

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)
Pages: 21 pages
Date: 2021-04-28
New Economics Papers: this item is included in nep-des and nep-sea
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