Reciprocal Preferences in Matching Markets

31 Pages Posted: 27 Feb 2023 Last revised: 21 Apr 2023

See all articles by Timm Opitz

Timm Opitz

Max Planck Institute for Innovation and Competition

Christoph Schwaiger

LMU - Ludwig Maximilians Universität Munich

Date Written: February 21, 2023

Abstract

Agents with reciprocal preferences prefer to be matched to a partner who also likes to collaborate with them. In this paper, we introduce and formalize reciprocal preferences, apply them to matching markets, and analyze the implications for mechanism design. Formally, the preferences of an agent can depend on the preferences of potential partners and there is incomplete information about the
partners’ preferences. We find that there is no stable mechanism in standard two-sided markets. Observing the final allocation of the mechanism enables agents to learn about each other’s preferences, leading to instability. However, in a school choice setting with one side of the market being non-strategic, modified versions of the deferred acceptance mechanism can achieve stability. These results provide insights into non-standard preferences in matching markets, and their implications for efficient information and mechanism design.

Keywords: Market Design, Matching, Reciprocal Preferences, Non-standard Preferences, Gale-Shapley Deferred Acceptance Mechanism, Incomplete Information

JEL Classification: C78, D47, D82, D83, D91

Suggested Citation

Opitz, Timm and Schwaiger, Christoph, Reciprocal Preferences in Matching Markets (February 21, 2023). Max Planck Institute for Innovation & Competition Research Paper No. 23-06, CRC TRR 190 Discussion Paper Series No. 388, Available at SSRN: https://ssrn.com/abstract=4365472

Timm Opitz (Contact Author)

Max Planck Institute for Innovation and Competition ( email )

Marstallplatz 1
Munich, Bayern 80539
Germany

Christoph Schwaiger

LMU - Ludwig Maximilians Universität Munich ( email )

Germany

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