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Paths to stability and uniqueness in two-sided matching markets

Author

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  • Vinay Ramani

    (Indian Institute of Management Udaipur, Mohanlal Sukhadia University Campus)

  • K. S. Mallikarjuna Rao

    (Indian Institute of Technology Bombay)

Abstract

The deferred acceptance algorithm introduced by Gale and Shapley is a centralized algorithm, where a social planner solicits the preferences from two sides of a market and generates a stable matching. On the other hand, the algorithm proposed by Knuth is a decentralized algorithm. In this article, we discuss conditions leading to the convergence of Knuth’s decentralized algorithm. In particular, we show that Knuth’s decentralized algorithm converges to a stable matching if either the Sequential Preference Condition (SPC) holds or if the market admits no cycle. In fact, acyclicity turns out to be a special case of SPC. We then consider markets where agents may prefer to remain single rather than being matched with someone. We introduce a generalized version of SPC for such markets. Under this notion of generalized SPC, we show that the market admits a unique stable matching, and that Knuth’s decentralized algorithm converges. The generalized SPC seems to be the most general condition available in the literature for uniqueness in two-sided matching markets.

Suggested Citation

  • Vinay Ramani & K. S. Mallikarjuna Rao, 2018. "Paths to stability and uniqueness in two-sided matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1137-1150, November.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:4:d:10.1007_s00182-017-0603-9
    DOI: 10.1007/s00182-017-0603-9
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    References listed on IDEAS

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    1. Kimmo Eriksson & Olle Häggström, 2008. "Instability of matchings in decentralized markets with various preference structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 409-420, March.
    2. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-30, December.
    3. Lauermann, Stephan & Nöldeke, Georg, 2014. "Stable marriages and search frictions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 163-195.
    4. Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 587-600, September.
    5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    6. Bettina Klaus & Flip Klijn, 2007. "Corrigendum to “On randomized matching mechanisms” [Economic Theory 8(1996)377–381]," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 411-416, August.
    7. 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.
    8. Jaeok Park, 2017. "Competitive equilibrium and singleton cores in generalized matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 487-509, May.
    9. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 377-381, August.
    10. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
    11. Becker, Gary S, 1974. "A Theory of Marriage: Part II," Journal of Political Economy, University of Chicago Press, vol. 82(2), pages 11-26, Part II, .
    12. Gary S. Becker, 1974. "A Theory of Marriage," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 299-351, National Bureau of Economic Research, Inc.
    13. 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.
    14. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    Cited by:

    1. Karpov, Alexander, 2019. "A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem," Economics Letters, Elsevier, vol. 178(C), pages 63-65.

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