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Random paths to stability in the roommate problem

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  • Diamantoudi, Effrosyni
  • Miyagawa, Eiichi
  • Xue, Licun

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 48 (2004)
Issue (Month): 1 (July)
Pages: 18-28

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Handle: RePEc:eee:gamebe:v:48:y:2004:i:1:p:18-28

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Jinpeng Ma, 1996. "On randomized matching mechanisms (*)," Economic Theory, Springer, vol. 8(2), pages 377-381.
  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. 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.
  5. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  6. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
  7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  8. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
  9. Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
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