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d-dimensional stable matching with cyclic preferences

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  • Hofbauer, Johannes

Abstract

Gale and Shapley (1962) have shown that in marriage markets, where men and women have preferences over potential partners of the other gender, a stable matching always exists. In this paper, we study a more general framework with d different genders due to Knuth (1976). The genders are ordered in a directed cycle and agents only have preferences over agents of the subsequent gender. Agents are then matched into families, which contain exactly one agent of each gender. We show that there always exists a stable matching if there are at most d+1 agents per gender, thereby generalizing and extending previous results. The proof is constructive and computationally efficient.

Suggested Citation

  • Hofbauer, Johannes, 2016. "d-dimensional stable matching with cyclic preferences," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 72-76.
    • Handle: RePEc:eee:matsoc:v:82:y:2016:i:c:p:72-76
    DOI: 10.1016/j.mathsocsci.2016.04.006
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    References listed on IDEAS

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    1. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
    2. Eriksson, Kimmo & Sjostrand, Jonas & Strimling, Pontus, 2006. "Three-dimensional stable matching with cyclic preferences," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 77-87, July.
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    Cited by:

    1. Niclas Boehmer & Edith Elkind, 2020. "Stable Roommate Problem with Diversity Preferences," Papers 2004.14640, arXiv.org.

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