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Stable matching games

Author

Listed:
  • Felipe Garrido-Lucero

    (IRIT, Université Toulouse Capitole)

  • Rida Laraki

    (Moroccan Center for Game Theory, UM6P)

Abstract

Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both improve their utility by forming a new pair. They proved, algorithmically, the existence of a stable matching. Shapley and Shubik, Demange and Gale, and many others extended the model by allowing monetary transfers. We offer a further extension by assuming that matched couples obtain their payoff endogenously as the outcome of a strategic game they have to play in a usual non-cooperative sense (without commitment) or in a semi-cooperative way (with commitment, as the outcome of a bilateral binding contract in which each player is responsible for her part of the contract). Depending on whether the players can commit or not, we define in each case a solution concept that combines Gale-Shapley pairwise stability with a (generalized) Nash equilibrium stability. In each case we give necessary and sufficient conditions for the set of solutions to be non-empty and provide an algorithm to compute a solution.

Suggested Citation

  • Felipe Garrido-Lucero & Rida Laraki, 2025. "Stable matching games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(3), pages 543-581, November.
    • Handle: RePEc:spr:sochwe:v:65:y:2025:i:3:d:10.1007_s00355-024-01577-4
    DOI: 10.1007/s00355-024-01577-4
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