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

A. Galichon and A. Jacquet

Games and Economic Behavior, 2025, vol. 152, issue C, 333-344

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:152:y:2025:i:c:p:333-344

DOI: 10.1016/j.geb.2025.05.004

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