An Impossibility Theorem in Matching Problems

17 Pages Posted: 13 Dec 2006

See all articles by Shohei Takagi

Shohei Takagi

Osaka University - Graduate School of Economics

Shigehiro Serizawa

Osaka University - Institute of Social and Economic Research (ISER)

Date Written: December 2006

Abstract

This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to matching problems. Alcalde and Barberá (1994) show that efficient and individually rational matching rules are manipulable in the one-to-one matching model. We pursue the possibility of strategy-proof matching rules by relaxing efficiency to the weaker condition of respect for unanimity. Our first result is positive. We prove that a strategy-proof rule exists that is individually rational and respects unanimity. However, this rule is unreasonable in the sense that a pair of agents who are the best for each other are matched on only rare occasions. In order to explore the possibility of better matching rules, we introduce the natural condition of "respect for pairwise unanimity." Respect for pairwise unanimity states that a pair of agents who are the best for each other should be matched, and an agent wishing to stay single should stay single. Our second result is negative. We prove that no strategy-proof rule exists that respects pairwise unanimity. This result implies Roth (1982) showing that stable rules are manipulable. We then extend this to the many-to-one matching model.

Keywords: Matching problems, Strategy-proofness

JEL Classification: C78, D71, D78

Suggested Citation

Takagi, Shohei and Serizawa, Shigehiro, An Impossibility Theorem in Matching Problems (December 2006). ISER Discussion Paper No. 677, Available at SSRN: https://ssrn.com/abstract=951136 or http://dx.doi.org/10.2139/ssrn.951136

Shohei Takagi

Osaka University - Graduate School of Economics ( email )

1-7 Machikaneyama
Toyonaka, Osaka, 560-0043
Japan

Shigehiro Serizawa (Contact Author)

Osaka University - Institute of Social and Economic Research (ISER) ( email )

6-1 Mihogaoka
Ibaraki, Osaka 567-0047
Japan
+81 6 6879 8558 (Phone)
+81 6 6878 2766 (Fax)

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