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# Monotonicity and Nash implementation in matching markets with contracts

Haake C-J, Klaus B (2005)
IMW working papers, Bielefeld: Universität Bielefeld.
256.34 KB
Working Paper | Published | English

Authors
UniBi ;
Department
Institut für mathematische Wirtschaftsforschung
Abstract

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.

Keywords
Matching with contracts ; (Maskin) monotonicity ; Nash implementation ; Stability
Year
2005
ISSN
0931-6558
File Name
372.pdf 256.34 KB
Access Level
Open Access

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##### Cite this
Haake C-J, Klaus B. Monotonicity and Nash implementation in matching markets with contracts. IMW working papers. Bielefeld: Universität Bielefeld; 2005.
Haake, C. - J., & Klaus, B. (2005). Monotonicity and Nash implementation in matching markets with contracts (IMW working papers) . Bielefeld: Universität Bielefeld.
Haake, C. - J., and Klaus, B. (2005). Monotonicity and Nash implementation in matching markets with contracts. IMW working papers, Bielefeld: Universität Bielefeld.
Haake, C.-J., & Klaus, B., 2005. Monotonicity and Nash implementation in matching markets with contracts, IMW working papers, Bielefeld: Universität Bielefeld.
C.-J. Haake and B. Klaus, Monotonicity and Nash implementation in matching markets with contracts, IMW working papers, Bielefeld: Universität Bielefeld, 2005.
Haake, C.-J., Klaus, B.: Monotonicity and Nash implementation in matching markets with contracts. IMW working papers. Universität Bielefeld, Bielefeld (2005).
Haake, Claus-Jochen, and Klaus, Bettina. Monotonicity and Nash implementation in matching markets with contracts. Bielefeld: Universität Bielefeld, 2005. IMW working papers.
@misc{2315479,
abstract     = {We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.},
author       = {Haake, Claus-Jochen and Klaus, Bettina},
issn         = {0931-6558},
language     = {English},
number       = {372},
publisher    = {Universit{\"a}t Bielefeld},
title        = {Monotonicity and Nash implementation in matching markets with contracts},
url          = {http://www.imw.uni-bielefeld.de/papers/files/imw-wp-372.pdf},
year         = {2005},
}


TY  - GEN
AB  - We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.
AU  - Haake, Claus-Jochen
AU  - Klaus, Bettina
ID  - 2315479
IS  - 372
KW  - Matching with contracts
KW  - Nash implementation
KW  - Stability
PB  - Universität Bielefeld
PY  - 2005
SN  - 0931-6558
TI  - Monotonicity and Nash implementation in matching markets with contracts
U3  - PUB:ID 2315479
UR  - http://nbn-resolving.de/urn:nbn:de:hbz:361-7662
ER  -

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