TY - JOUR
T1 - The matching problem with linear transfers is equivalent to a hide-and-seek game
AU - Galichon, A.
AU - Jacquet, A.
N1 - Publisher Copyright:
© 2025 The Author(s)
PY - 2025/7
Y1 - 2025/7
N2 - 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.
AB - 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.
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U2 - 10.1016/j.geb.2025.05.004
DO - 10.1016/j.geb.2025.05.004
M3 - Article
AN - SCOPUS:105005087292
SN - 0899-8256
VL - 152
SP - 333
EP - 344
JO - Games and Economic Behavior
JF - Games and Economic Behavior
ER -