Stability and strategy-proofness for matching with interval constraints

Tsuyoshi Adachi () and Yuki Ishibashi
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Tsuyoshi Adachi: Faculty of Political Science and Economics, Waseda University
Yuki Ishibashi: Graduate School of Economics, Waseda University

No 2124, Working Papers from Waseda University, Faculty of Political Science and Economics

Abstract: We consider a matching problem with interval constraints under the hierarchical region structure. We proposes new stability, interval respecting stability, for matching problems with interval constraints, which defines ceiling respecting stability (Kamada and Kojima, 2018) using a blocking coalition instead of a pair, following floor respecting stability (Akin, 2021). Interval respecting stability coincides with floor respecting stability in problems with floor constraints and implies ceiling respecting stability in problems with ceiling constraints. In addition, interval respecting stability generally implies Pareto efficiency, unlike ceiling respecting stability. We also propose a generalized flexible deferred acceptance algorithm for a problem with interval constraints, which is a flexible deferred acceptance algorithm (i.e., cumulative offer process) that allocates quotas between regions, reserving additional numbers for doctors’ future offers needed to fill the floor constraints even if there are no offers now. Under acceptability, we show that further combining the above algorithm with the serial dictatorship yields an algorithm that satisfies interval respecting stability. We also show that the combinded algorithm is strategy-proof for doctors.

Keywords: Matching; Interval constraints; Stability; Strategy-proofness; Cumulative offer process (search for similar items in EconPapers)
JEL-codes: C78 D47 D61 D63 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2022-03
New Economics Papers: this item is included in nep-des and nep-ore
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