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

Alfred Galichon; Antoine Jacquet

doi:10.1016/j.geb.2025.05.004

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arXiv · 2402.12200

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

Alfred Galichon·Antoine Jacquet

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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 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.

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Alfred Galichon, Antoine Jacquet. 2024-02-19. The matching problem with linear transfers is equivalent to a hide-and-seek game. https://doi.org/10.1016/j.geb.2025.05.004

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