Work

The matching problem with linear transfers is equivalent to a hide-and-seek game

Year: 2025

Type: article

Abstract: Matching problems with linearly transferable utility (LTU) generalize the well-studied transferable utility (TU) case by relaxing the assumption that utility is transferred one-for-one within matched pairs. We show that LTU matching problems can be reframed as nonzero-sum hide-and-seek games between two players, thus generalizing a result from von Neumann . The underlying linear programming structure of TU matching problems, however, is lost when moving to LTU. These results draw a new bridge between non-TU matching problems and the theory of bimatrix games, with consequences notably regarding the computation of stable outcomes.

Source: Games and Economic Behavior

DOI: 10.1016/j.geb.2025.05.004

Authors: A. Galichon, A. Jacquet

Institutions: Institut d'Etudes Politiques de Paris, Département d'économie de Sciences Po, New York University

Language: English

Topic: Game Theory and Voting Systems

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

Funder: European Research Council