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Punishment-Dominance Condition on Stable Two-Sided Matching Algorithms

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  • Takuya Masuzawa

    (Faculty of Economics, Keio University)

Abstract

In this article, we consider a many-to-one two-sided matching market and define a canonical strategic form game, in which any worker applies to the top k firms and is assigned to the most preferred firm that does not reject him/her. Under the substitute property of firms' preferences, the game satisfies the punishment-dominance condition. The deferred-acceptance algorithm by Gale and Shapley (Amer. Math. Monthly 69: 1962), which finds the maximum and minimum of stable matchings, is described as an instance of the algorithm by Masuzawa (Int. Jour. Game Theory 38: 2008), which determines the α-cores of the strategic form games with the punishment-dominance condition.

Suggested Citation

  • Takuya Masuzawa, 2012. "Punishment-Dominance Condition on Stable Two-Sided Matching Algorithms," Keio/Kyoto Joint Global COE Discussion Paper Series 2012-018, Keio/Kyoto Joint Global COE Program.
    • Handle: RePEc:kei:dpaper:2012-018
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    References listed on IDEAS

    as
    1. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    2. Takuya Masuzawa, 2008. "Computing the cores of strategic games with punishment–dominance relations," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 185-201, June.
    3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    4. 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.
    5. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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