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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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    Cited by:

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