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

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  • Alfred Galichon
  • Antoine Jacquet

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.

Suggested Citation

  • Alfred Galichon & Antoine Jacquet, 2024. "The matching problem with linear transfers is equivalent to a hide-and-seek game," Papers 2402.12200, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2402.12200
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    References listed on IDEAS

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    1. Patrick Legros & Andrew F. Newman, 2007. "Beauty Is a Beast, Frog Is a Prince: Assortative Matching with Nontransferabilities," Econometrica, Econometric Society, vol. 75(4), pages 1073-1102, July.
    2. Patrick Legros & Andrew Newman, 2007. "Beauty is a beast, frog is a prince :assortative matching in a nontransferable world," ULB Institutional Repository 2013/7022, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. Ilan Adler & Martin Bullinger & Vijay V. Vazirani, 2024. "A Generalization of von Neumann's Reduction from the Assignment Problem to Zero-Sum Games," Papers 2410.10767, arXiv.org, revised Jan 2026.

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