Stability and Nash Implementation in Matching Markets with Couples

Jochen Haake, Claus; Klaus, Bettina-Elisabeth

doi:10.2139/ssrn.1235462

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Stability and Nash Implementation in Matching Markets with Couples

Harvard Business School NOM Working Paper No. 09-017

17 Pages Posted: 19 Aug 2008

See all articles by Claus Jochen Haake

Bettina-Elisabeth Klaus

University of Lausanne

Date Written: August 18, 2008

Abstract

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable.

Keywords: Matching with Couples, (Maskin) Monotonicity, Nash Implementation, Stability, Weakly Responsive Preferences

JEL Classification: C62, C78, D78, J41

Suggested Citation: Suggested Citation

Jochen Haake, Claus and Klaus, Bettina-Elisabeth, Stability and Nash Implementation in Matching Markets with Couples (August 18, 2008). Harvard Business School NOM Working Paper No. 09-017, Available at SSRN: https://ssrn.com/abstract=1235462 or http://dx.doi.org/10.2139/ssrn.1235462