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Stochastic stability for roommate markets

  • Klaus, Bettina
  • Klijn, Flip
  • Walzl, Markus

We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 6 (November)
Pages: 2218-2240

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2218-2240
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. 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.
  2. Bochet Olivier & Klaus Bettina & Walzl Markus, 2007. "Dynamic Recontracting processes with Multiple Indivisible Goods," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Klaus Bettina & Klijn Flip, 2007. "Smith and Rawls Share a Room," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer, vol. 36(3), pages 461-471, March.
  5. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer, vol. 35(4), pages 647-667, October.
  6. 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.
  7. Roberto Serrano & Oscar Volij, 2003. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economics Working Papers 0029, Institute for Advanced Study, School of Social Science.
  8. 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.
  9. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March.
  10. INARRA, Elena & LARREA, Conchi & MOLIS, Elena, 2010. "The stability of the roommate problem revisited," CORE Discussion Papers 2010007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  12. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
  13. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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