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Random paths to stability in the roommate problem

  • Effrosyni Diamantoudi

    ()

    (Concordia University - Department of Economics)

  • Eiichi Miyagawa

    ()

    (Columbia University - Department of Economics)

  • Licun Xue

    ()

    (McGill University - Department of Economics)

This paper studies whether a sequence of myopic blockings leads to a stable matching in the roommate problem. We prove that if a stable matching exists and preferences are strict, then for any unstable matching, there exists a finite sequence of successive myopic blockings leading to a stable matching. This implies that, starting from any unstable matching, the process of allowing a randomly chosen blocking pair to form converges to a stable matching with probability one. This result generalizes those of Roth and Vande Vate (1990) and Chung (2000)under strict preferences.

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File URL: http://www.econ.columbia.edu/RePEc/pdf/DP0102-65.pdf
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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0102-65.

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Length: 15 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:clu:wpaper:0102-65
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  1. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
  2. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
  3. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  4. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
  5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  6. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer, vol. 8(2), pages 377-81, August.
  7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
  8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  9. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
  10. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
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