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# Stability and Nash implementation in matching markets with couples

Haake C-J, Klaus B (2008)
Working Papers. Institute of Mathematical Economics, 399. Bielefeld: Universität Bielefeld.
295.41 KB
Working Paper | Published | English

Authors
UniBi ;
Department
Institut für mathematische Wirtschaftsforschung
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
Stability ; Nash implementation ; Matching with couples ; (Maskin) monotonicity ; Weakly responsive preferences
Year
2008
ISSN
0931-6558
File Name
399.pdf 295.41 KB
MD5 Checksum
8291064a48cc2d5fb516ddf744b2c665
Access Level
Open Access

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##### Cite this
Haake C-J, Klaus B. Stability and Nash implementation in matching markets with couples. Working Papers. Institute of Mathematical Economics. Vol 399. Bielefeld: Universität Bielefeld; 2008.
Haake, C. - J., & Klaus, B. (2008). Stability and Nash implementation in matching markets with couples (Working Papers. Institute of Mathematical Economics, 399) . Bielefeld: Universität Bielefeld.
Haake, C. - J., and Klaus, B. (2008). Stability and Nash implementation in matching markets with couples. Working Papers. Institute of Mathematical Economics, 399, Bielefeld: Universität Bielefeld.
Haake, C.-J., & Klaus, B., 2008. Stability and Nash implementation in matching markets with couples, Working Papers. Institute of Mathematical Economics, no.399, Bielefeld: Universität Bielefeld.
C.-J. Haake and B. Klaus, Stability and Nash implementation in matching markets with couples, Working Papers. Institute of Mathematical Economics, vol. 399, Bielefeld: Universität Bielefeld, 2008.
Haake, C.-J., Klaus, B.: Stability and Nash implementation in matching markets with couples. Working Papers. Institute of Mathematical Economics, 399. Universität Bielefeld, Bielefeld (2008).
Haake, Claus-Jochen, and Klaus, Bettina. Stability and Nash implementation in matching markets with couples. Bielefeld: Universität Bielefeld, 2008. Working Papers. Institute of Mathematical Economics. 399.
@misc{2315850,
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 {\textacutedbl}double stable{\textacutedbl} 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.},
author       = {Haake, Claus-Jochen and Klaus, Bettina},
issn         = {0931-6558},
language     = {English},
publisher    = {Universit{\"a}t Bielefeld},
title        = {Stability and Nash implementation in matching markets with couples},
url          = {http://www.imw.uni-bielefeld.de/papers/files/imw-wp-399.pdf},
volume       = {399},
year         = {2008},
}


TY  - GEN
AB  - 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.
AU  - Haake, Claus-Jochen
AU  - Klaus, Bettina
ID  - 2315850
KW  - Stability
KW  - Nash implementation
KW  - Matching with couples
KW  - Weakly responsive preferences
PB  - Universität Bielefeld
PY  - 2008
SN  - 0931-6558
TI  - Stability and Nash implementation in matching markets with couples
U3  - PUB:ID 2315850
UR  - http://nbn-resolving.de/urn:nbn:de:hbz:361-13473
VL  - 399
ER  -

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