Ranking by Manipulability and Quantile Stable Mechanisms

26 Pages Posted: 1 Jan 2013 Last revised: 14 Aug 2014

See all articles by Peter Chen

Peter Chen

McKinsey & Co. Inc.

Michael Egesdal

Airbnb

Marek Pycia

University of Zurich

M. Bumin Yenmez

Boston College

Date Written: August 1, 2014

Abstract

We study manipulability of stable matching mechanisms and show that manipulability comparisons are equivalent to preference comparisons: for any agent, a mechanism is more manipulable than another if and only if this agent prefers the latter to the former. In particular, this implies that no two stable mechanisms can be ranked in terms of manipulability for all agents. We then construct quantile stable mechanisms, establish conditions under which they are well defined, and observe that they can be ranked in terms of manipulability for one side of the market, but not for both. In particular, the typically used mechanism that selects the stable matching that is best for one side of the market has no incentive advantage over other quantile stable mechanisms when both sides of the market are strategic. As an auxiliary result, we provide sufficient conditions for the existence of median stable matchings, and more generally, show that quantile stable matchings exist when contracts are strong substitutes and satisfy the law of aggregate demand. This last result is of independent interest as experiments show that agents who match in a decentralized way tend to coordinate on the median stable matching, when it exists.

Keywords: Matching with Contracts, Median Stable Matchings, Strong Substitutes, Law of Aggregate Demand

JEL Classification: C78, D47

Suggested Citation

Chen, Peter and Egesdal, Michael and Pycia, Marek and Yenmez, M. Bumin, Ranking by Manipulability and Quantile Stable Mechanisms (August 1, 2014). Available at SSRN: https://ssrn.com/abstract=2194458 or http://dx.doi.org/10.2139/ssrn.2194458

Peter Chen

McKinsey & Co. Inc. ( email )

Konigsallee 60C
Chicago, IL Quebec 60603
United States

Michael Egesdal

Airbnb ( email )

888 Brannan St
San Francisco, CA 94103
United States

Marek Pycia (Contact Author)

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

M. Bumin Yenmez

Boston College ( email )

140 Commonwealth Ave.
Maloney Hall 327
Chestnut Hill, MA 02467
United States

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