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Stochastic Stability for Roommate Markets

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  • Bettina Klaus
  • Flip Klijn
  • Markus Walzl

Abstract

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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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 357.

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Date of creation: May 2008
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Handle: RePEc:bge:wpaper:357

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Keywords: core; (pairwise) stability; roommate markets; stochastic stability;

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References

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  1. Bettina Klaus & Flip Klijn, 2009. "Smith and Rawls Share a Room: Stability and Medians," Harvard Business School Working Papers, Harvard Business School 09-111, Harvard Business School.
  2. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics, Boston College Department of Economics 449, Boston College Department of Economics.
  3. BOCHET, Olivier & KLAUS, Bettina & WALZL, Markus, 2007. "Dynamic recontracting processes with multiple indivisible goods," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2007061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Roberto Serrano & Oscar Volij, 2003. "MISTAKE IN COOPERATION:the Stochastic Stability of Edgeworth's Recontracting," Working Papers 2003-23, Brown University, Department of Economics.
  5. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer, Springer, vol. 36(3), pages 461-471, March.
  6. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 706.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  7. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, Elsevier, vol. 48(1), pages 18-28, July.
  8. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, Elsevier, vol. 106(2), pages 265-295, October.
  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, Springer, vol. 36(3), pages 473-488, March.
  10. Larrea Jaurrieta, María Concepción & Iñarra García, María Elena & Molis Bañales, Elena, 2007. "The Stability of the Roommate Problem Revisited," IKERLANAK, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I 2007-30, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  12. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1475-80, November.
  13. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 38(2), pages 201-230, February.
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Citations

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Cited by:
  1. Péter Biró & Gethin Norman, 2013. "Analysis of stochastic matching markets," International Journal of Game Theory, Springer, Springer, vol. 42(4), pages 1021-1040, November.
  2. repec:pdn:wpaper:74 is not listed on IDEAS
  3. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers Dissertations 02, University of Paderborn, Faculty of Business Administration and Economics.
  4. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, Elsevier, vol. 59(3), pages 360-363, May.
  5. Klaus, Bettina & Newton, Jonathan, 2014. "Stochastic Stability in Assignment Problems," Working Papers, University of Sydney, School of Economics 2014-05, University of Sydney, School of Economics.
  6. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.
  7. Boncinelli, Leonardo & Pin, Paolo, 2014. "Efficiency and Stability in a Process of Teams Formation," MPRA Paper 56356, University Library of Munich, Germany.
  8. Newton, Jonathan & Sawa, Ryoji, 2013. "A one-shot deviation principle for stability in matching problems," Working Papers, University of Sydney, School of Economics 2013-09, University of Sydney, School of Economics, revised Jul 2014.
  9. Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, Elsevier, vol. 81(C), pages 165-178.

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