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

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  • Galichon, A.
  • Jacquet, A.

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.

Suggested Citation

  • Galichon, A. & Jacquet, A., 2025. "The matching problem with linear transfers is equivalent to a hide-and-seek game," Games and Economic Behavior, Elsevier, vol. 152(C), pages 333-344.
    • Handle: RePEc:eee:gamebe:v:152:y:2025:i:c:p:333-344
    DOI: 10.1016/j.geb.2025.05.004
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    References listed on IDEAS

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