Stability against Robust Deviations in the Roommate Problem

61 Pages Posted: 6 Apr 2020

See all articles by Daisuke Hirata

Daisuke Hirata

Hitotsubashi University

Yusuke Kasuya

Kobe University - Faculty of Economics

Kentaro Tomoeda

University of Technology Sydney (UTS) - Department of Economics

Date Written: March 11, 2020

Abstract

We propose a new solution concept in the roommate problem, based on the "robustness" of deviations (i.e., blocking coalitions). We call a deviation from a matching robust up to depth k, if none of the deviators gets worse off than at the original matching after any sequence of at most k subsequent deviations. We say that a matching is stable against robust deviations (for short, SaRD) up to depth k, if there is no robust deviation up to depth k. As a smaller k imposes a stronger requirement for a matching to be SaRD, we investigate the existence of a matching that is SaRD with a minimal depth k. We constructively demonstrate that a SaRD matching always exists for k=3, and establish sufficient conditions for k=1 and 2.

Suggested Citation

Hirata, Daisuke and Kasuya, Yusuke and Tomoeda, Kentaro, Stability against Robust Deviations in the Roommate Problem (March 11, 2020). Available at SSRN: https://ssrn.com/abstract=3552365 or http://dx.doi.org/10.2139/ssrn.3552365

Daisuke Hirata (Contact Author)

Hitotsubashi University ( email )

2-1 Naka Kunitachi-shi
Tokyo 186-8601
Japan

Yusuke Kasuya

Kobe University - Faculty of Economics ( email )

2-1, Rokkodai
Nada-Ku
Kobe, Hyogo, 657-8501
Japan

Kentaro Tomoeda

University of Technology Sydney (UTS) - Department of Economics ( email )

Sydney
Australia

HOME PAGE: http://sites.google.com/site/kentarotomoeda/

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