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Matchings under Stability, Minimum Regret, and Forced and Forbidden Pairs in Marriage Problem

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  • Mandal, Pinaki
  • Roy, Souvik

Abstract

We provide a class of algorithms, called men-women proposing deferred acceptance (MWPDA) algorithms, that can produce all stable matchings at every preference profile for the marriage problem. Next, we provide an algorithm that produces a minimum regret stable matching at every preference profile. We also show that its outcome is always women-optimal in the set of all minimum regret stable matchings. Finally, we provide an algorithm that produces a stable matching with given sets of forced and forbidden pairs at every preference profile, whenever such a matching exists. As before, here too we show that the outcome of the said algorithm is women-optimal in the set of all stable matchings with given sets of forced and forbidden pairs.

Suggested Citation

  • Mandal, Pinaki & Roy, Souvik, 2021. "Matchings under Stability, Minimum Regret, and Forced and Forbidden Pairs in Marriage Problem," MPRA Paper 107213, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:107213
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    References listed on IDEAS

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    1. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
    2. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    3. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    4. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-570, May.
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    JEL classification:

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

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