Robust Minimal Instability of the Top Trading Cycles Mechanism

21 Pages Posted: 7 Apr 2020 Last revised: 9 Apr 2020

See all articles by Battal Dogan

Battal Dogan

Department of Economics, University of Bristol

Lars Ehlers

University of Montreal - D├ępartement de Sciences Economiques and CIREQ

Date Written: April 2, 2020

Abstract

In the context of priority-based resource allocation, we formulate methods to compare assignments in terms of their stability as binary relations (on the set of possible assignments) that depend on the preference and the priority profile. We introduce three basic properties, stability preferred, separability, and consistency, that a reasonable stability comparison should satisfy. We show that, for any stability comparison satisfying the three properties, the top trading cycles (TTC) mechanism is minimally unstable among efficient and strategy-proof mechanisms in one-to-one matching. An important consequence is the robustness of a recent result by Abdulkadiroglu et al. (2019), which uses a particular stability comparison method where an assignment is more stable than another assignment if the set of blocking pairs in the former assignment is a subset of the set of blocking pairs in the latter assignment. Our unifying approach covers basically all natural comparison methods and it includes many cardinal stability comparison methods as special cases.

Suggested Citation

Dogan, Battal and Ehlers, Lars, Robust Minimal Instability of the Top Trading Cycles Mechanism (April 2, 2020). Available at SSRN: https://ssrn.com/abstract=3555762 or http://dx.doi.org/10.2139/ssrn.3555762

Battal Dogan (Contact Author)

Department of Economics, University of Bristol ( email )

United Kingdom

Lars Ehlers

University of Montreal - D├ępartement de Sciences Economiques and CIREQ ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7
Canada

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