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Matching with Myopic and Farsighted Players

Author

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  • Herings, P. Jean-Jacques

    (General Economics 1 (Micro))

  • Mauleon, Ana

    (university of louvain, louvain la neuve)

  • Vannetelbosch, Vincent

    (university of louvain, louvain la neuve)

Abstract

We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the myopic-farsighted stable set, which is based on the notion of a myopic-farsighted improving path. A myopic-farsighted stable set is the set of matchings such that there is no myopic-farsighted improving path from any matching in the set to another matching in the set (internal stability) and there is a myopic-farsighted improving path from any matching outside the set to some matching in the set (external stability). For the special cases where all players are myopic and where all players are farsighted, our concept predicts the set of matchings in the core. When all men are myopic and the top choice of each man is a farsighted woman, we show that the singleton consisting of the woman-optimal stable matching is a myopic-farsighted stable set. The same result holds when all women are farsighted. We present examples where this is the unique myopic-farsighted stable set as well as examples of myopic-farsighted stable sets consisting of a core element different from the woman-optimal matching or even of a non-core element.

Suggested Citation

  • Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Matching with Myopic and Farsighted Players," Research Memorandum 011, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2017011
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    References listed on IDEAS

    as
    1. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    2. Ana Mauleon & Vincent Vannetelbosch, 2004. "Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers," Theory and Decision, Springer, vol. 56(3), pages 291-324, May.
    3. Francis Bloch & Anne van den Nouweland, 2017. "Farsighted Stability with Heterogeneous Expectations," Working Papers 2017.31, Fondazione Eni Enrico Mattei.
    4. Federico Echenique & Alistair J. Wilson & Leeat Yariv, 2016. "Clearinghouses for two‐sided matching: An experimental study," Quantitative Economics, Econometric Society, vol. 7(2), pages 449-482, July.
    5. John H. Kagel & Alvin E. Roth, 2000. "The Dynamics of Reorganization in Matching Markets: A Laboratory Experiment Motivated by a Natural Experiment," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 201-235.
    6. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    7. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    8. Nalbantian, Haig R & Schotter, Andrew, 1995. "Matching and Efficiency in the Baseball Free-Agent System: An Experimental Examination," Journal of Labor Economics, University of Chicago Press, vol. 13(1), pages 1-31, January.
    9. Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
    10. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    11. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
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    More about this item

    Keywords

    marriage problems; stable sets; myopic and farsighted players;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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