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Conditional Stable Matchings

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Abstract

In matching theory of contracts the substitutes condition plays an essential role to ensure the existence of stable matchings. We study many-to-many matchings where groups of individuals, of size possibly greater than two, are matched to a set of institutions. Real-world examples include orphan brothers accepting an adoptive family conditional on all of them being included; hiring contracts that may only be chosen together; or a situation where a firm accepts to hire several workers only if they accept to work on different days (part-time jobs). We demonstrate by several examples that such extra conditions may alter the natural choice maps so that stable matchings cannot be obtained by applying the standard theorems. We overcome this difficulty by introducing a new construction of choice maps. We prove that they yield stable matchings if the construction respects an "anti-trust" rule on the supply side of the market.

Suggested Citation

  • Vilmos Komornik & Christelle Viauroux, 2012. "Conditional Stable Matchings," UMBC Economics Department Working Papers 12-03, UMBC Department of Economics.
  • Handle: RePEc:umb:econwp:1203
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    File URL: http://www.umbc.edu/economics/wpapers/wp_12_03.pdf
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    References listed on IDEAS

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    1. Vilmos Komornik & Zsolt Komornik & Christelle Viauroux, 2010. "Stable Schedule Matchings," UMBC Economics Department Working Papers 10-120, UMBC Department of Economics, revised 01 Jul 2011.
    2. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
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    4. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    5. Bettina Klaus & Flip Klijn, 2007. "Fair and efficient student placement with couples," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 177-207, October.
    6. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    7. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
    8. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    9. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    10. 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.
    11. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
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    13. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.
    14. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
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    More about this item

    Keywords

    games; matchings; choice maps; blocs; substitutes condition;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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