From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution

Christian Trudeau

No 1506, Working Papers from University of Windsor, Department of Economics

Abstract: We revisit two classic problems: the assignment problem, in which agents create value when matched with a partner, and the bankruptcy problem, in which we need to share an endowment among agents with conflicting claims. We show that since Core Selection constrains us to exactly divide the value created by a pair of matched agents, the assignment problem can be seen as a two-player bankruptcy problem. This interpretation allows us to show that the classic Concede-and-Divide (Aumann and Maschler, 1985) sharing method for the bankruptcy problem is equivalent to the Fair Division solution (Thompson, 1981) for the assignment problem, itself the average of the extreme points of the core of Demange (1982) and Leonard (1983). We then exploit the link between the two problems to offer two characterizations of the Fair Division solution. The key property is an adapation of the Minimal Rights First property (Curiel, Maschler and Tijs, 1987) for the bankruptcy problem. The minimal rights of a claimant is what is left of the endowment, if any, when all claimants but himself have received their full claims. The property states that we obtain the same shares if we distribute the minimal rights first, adjust the claims and endowment and proceed on the reduced problem or simply ignore them and proceed on the original problem. In assignment problems, the conceptual equivalent of minimal rights are the minimal core allocations. Given the important role that minimal core allocations play in this link between assignment and bankruptcy problems, it is important to be able to compute them efficiently. We provide a new algorithm to compute them.

Keywords: assignment problems; bankruptcy problems; core; fair division; concede-and-divide; minimal rights. (search for similar items in EconPapers)
JEL-codes: C71 D63 (search for similar items in EconPapers)
Pages: 11 pages
Date: 2015-12
New Economics Papers: this item is included in nep-gth
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http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1506.pdf Second version, 2016 (application/pdf)

Related works:
Journal Article: From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:wis:wpaper:1506

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