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Stochastic Stability for Roommate Markets

  • Klaus Bettina
  • Klijn Flip
  • Walzl Markus

    (METEOR)

We show that for any roommate market the set of stochastically stable matchings coincideswith 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 beenproposed 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 onlysolution concept that is core consistent and shares the stochastic stability characteristic withthe core.

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File URL: http://digitalarchive.maastrichtuniversity.nl/fedora/objects/guid:d765c319-83c4-4c80-ac5a-d8f0aaa09e9a/datastreams/ASSET1/content
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Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 010.

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Date of creation: 2008
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Handle: RePEc:unm:umamet:2008010
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  1. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  2. 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).
  3. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," Working Papers 315, Barcelona Graduate School of Economics.
  4. M.Utku Unver & Fuhito Kojima, 2006. "Random Paths to Pairwise Stability in Many-to-Many Matching Problems: A Study on Market Equilibration," Working Papers 256, University of Pittsburgh, Department of Economics, revised Jan 2006.
  5. 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.
  6. Roberto Serrano & Oscar Volij, 2003. "MISTAKE IN COOPERATION:the Stochastic Stability of Edgeworth's Recontracting," Working Papers 2003-23, Brown University, Department of Economics.
  7. 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.
  8. 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.
  9. BOCHET, Olivier & KLAUS, Bettina & WALZL, Markus, 2007. "Dynamic recontracting processes with multiple indivisible goods," CORE Discussion Papers 2007061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. 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.
  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. 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.
  13. 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.
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