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Solving Becker's assortative assignments and extensions

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  • Martínez-de-Albéniz, F. Javier
  • Rafels, Carlos
  • Ybern, Neus

Abstract

We analyze assortative assignment games, introduced in Becker (1973) and Eriksson et al. (2000). We study the extreme core points and show an easy way to compute them. We find a natural solution for these games. It coincides with several well-known point solutions, the median stable utility solution (Schwarz and Yenmez, 2011) and the nucleolus (Schmeidler, 1969). We also analyze the behavior of the Shapley value. We finish with some extensions, where some hypotheses are relaxed.

Suggested Citation

  • Martínez-de-Albéniz, F. Javier & Rafels, Carlos & Ybern, Neus, 2019. "Solving Becker's assortative assignments and extensions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 248-261.
    • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:248-261
    DOI: 10.1016/j.geb.2018.09.005
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    References listed on IDEAS

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    1. Maike Hoffmann & Peter Sudhölter, 2007. "The Shapley value of exact assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 557-568, April.
    2. Chen, Peter & Egesdal, Michael & Pycia, Marek & Yenmez, M. Bumin, 2016. "Median stable matchings in two-sided markets," Games and Economic Behavior, Elsevier, vol. 97(C), pages 64-69.
    3. Francesc Llerena & Marina Nunez, 2011. "A geometric characterization of the nucleolus of the assignment game," Economics Bulletin, AccessEcon, vol. 31(4), pages 3275-3285.
    4. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    5. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Pere Villar, Joan, 2002. "Assignment Games Satisfy the CoMa-Property," Games and Economic Behavior, Elsevier, vol. 38(2), pages 231-239, February.
    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, vol. 146(2), pages 619-637, March.
    8. Katerina Sherstyuk, 1999. "Multisided matching games with complementarities," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 489-509.
    9. Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets with the same core," Games and Economic Behavior, Elsevier, vol. 73(2), pages 553-563.
    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. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    12. Núñez, Marina & Rafels, Carles, 2008. "On the dimension of the core of the assignment game," Games and Economic Behavior, Elsevier, vol. 64(1), pages 290-302, September.
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    1. Martínez-de-Albéniz, F. Javier & Rafels, Carlos & Ybern, Neus, 2020. "Assortative multisided assignment games: The extreme core points," Games and Economic Behavior, Elsevier, vol. 120(C), pages 144-153.

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    More about this item

    Keywords

    Assortative market; Assignment game; Core; Nucleolus;
    All these keywords.

    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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