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One-to-One Matching Problems with Location Restrictions

Author

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  • 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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    References listed on IDEAS

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    1. 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.
    2. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    3. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    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. Robert W. Irving, 2008. "Stable matching problems with exchange restrictions," Journal of Combinatorial Optimization, Springer, vol. 16(4), pages 344-360, November.
    6. 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.
    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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