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One-to-One Matching Problems with Location Restrictions

Author

Listed:
  • VERGOTE, W.

    (Université catholique de Louvain, CORE, Belgium)

Abstract

This paper introduces a novel set of one-to-one matching problems: matchings subject to location restrictions. When scarcity of matching locations exists some agents may want to form a new partnership without being able to implement it. In this general setting we develop two stability concepts, direct and (coalition) ex- change* stability, akin to Gale Shapley stability and exchange stability (Alcalde, 1995) respectively. We show that coalition-exchange* stability is a refinement of direct stability. When no location scarcity exists then direct stability is equivalent to Gale Shapley stability and coalition-exchange* stability is equivalent to requiring both exchange stability (Alcalde, 1995) and Gale Shapley stability. We show that the set of coalition-exchange* stable matchings is a superset of the farsighted core, and equal to the farsighted core if locations are not scarce and the matching problem is individually rational. The paper also shows that an exchange* stable set can not be a strict subset of a farsighted stable set and provides an example of a roommate problem in which no farsighted stable set exists while an exchange* stable set does exist. Finally, the paper obtains that deciding whether the farsighted core of an individually rational roommate problem exists is NP-complete.

Suggested Citation

  • Vergote, W., 2015. "One-to-One Matching Problems with Location Restrictions," LIDAM Discussion Papers CORE 2015054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2015054
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2015.html
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    References listed on IDEAS

    as
    1. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    2. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    3. Robert W. Irving, 2008. "Stable matching problems with exchange restrictions," Journal of Combinatorial Optimization, Springer, vol. 16(4), pages 344-360, November.
    4. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
    5. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    One-to-one Matching; Direct Dominance; Exchange Dominance; Indirect Dominance;
    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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