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Random Paths to Popularity in Two-Sided Matching

Author

Listed:
  • Aleksei Yu. Kondratev

    (National Research University Higher School of Economics)

  • Alexander S. Nesterov

    (National Research University Higher School of Economics)

Abstract

We study practically relevant aspects of popularity in two-sided matching where only one side has preferences. A matching is called popular if there does not exist another matching that is preferred by a simple majority. We show that for a matching to be popular it is necessary and sucient that no coalition of size up to 3 decides to exchange their houses by simple majority.We then constructively show that a market where such coalitions meet at random converges to a popular matching whenever it exists.

Suggested Citation

  • Aleksei Yu. Kondratev & Alexander S. Nesterov, 2018. "Random Paths to Popularity in Two-Sided Matching," HSE Working papers WP BRP 195/EC/2018, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:195/ec/2018
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    References listed on IDEAS

    as
    1. Eric McDermid & Robert W. Irving, 2011. "Popular matchings: structure and algorithms," Journal of Combinatorial Optimization, Springer, vol. 22(3), pages 339-358, October.
    2. Agnes Cseh & Chien-Chung Huang & Telikepalli Kavitha, 2017. "Popular matchings with two-sided preferences and one-sided ties," CERS-IE WORKING PAPERS 1723, Institute of Economics, Centre for Economic and Regional Studies.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    two-sided matching; popular matching; random paths; house allocation; assignment problem;
    All these keywords.

    JEL classification:

    • Z - Other Special Topics

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