Constrained random matching

Ivan Balbuzanov

Journal of Economic Theory, 2022, vol. 203, issue C

Abstract: This paper generalizes the Probabilistic Serial (PS) mechanism of Bogomolnaia and Moulin (2001) to matching markets with arbitrary constraints. The constraints are modeled as a set of permissible ex post allocations. A result of independent interest gives a simple geometric characterization of all lotteries over the set of permissible allocations: they are the ones that satisfy a collection of simple and tractable linear inequalities determined by the constraints. The inequalities correspond to the hyperplanes defining a convex polytope that is intuitively constructed from the given set. When a general version of the PS algorithm is executed under these inequalities, the outcome is an efficient and fair lottery over the set of permissible allocations. The method is general, can be applied to both one-sided and two-sided matching markets, and allows for multi-unit demand.

Keywords: Constrained random assignment; Probabilistic serial mechanism; sd-efficiency; Fairness (search for similar items in EconPapers)
JEL-codes: C78 D82 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:203:y:2022:i:c:s002205312200062x

DOI: 10.1016/j.jet.2022.105472

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