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Stable Matchings for a Generalised Marriage Problem

Author

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  • Somdeb Lahiri

    (School of Economic and Business Sciences, University of Witwatersrand at Johannesburg)

Abstract

We show that a simple generalisation of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley (1962) yields outcomes for a generalised marriage problem, which are necessarily stable. We also show that any outcome of this procedure is Weakly Pareto Optimal for Men, i.e. there is no other outcome which all men prefer to an outcome of this procedure. In a final concluding section of this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of feasible contracts to choose from. We call such problems, generalised contract choice problems. The model we propose is a generalisation of the model due to Shapley and Scarf (1974) called the housing market. We are able to show with the help of a three agent example, that there exists a generalised contract choice problem, which does not admit any stable outcome.

Suggested Citation

  • Somdeb Lahiri, 2003. "Stable Matchings for a Generalised Marriage Problem," Working Papers 2003.117, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2003.117
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    File URL: https://www.feem.it/m/publications_pages/NDL2003-117.pdf
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    Cited by:

    1. Lahiri, S., 2004. "Stable outcomes for contract choice problems," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 15(4), pages 409-418.

    More about this item

    Keywords

    Stable outcomes; Matchings; pay-offs; Generalised marriage problem; Contract choice problem;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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