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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. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  2. 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.
  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. 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. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
  6. 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.
  7. 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).
  8. 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).
  9. 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.
  10. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  11. 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.
  12. 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.
  13. 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.
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Cited by:
  1. Bettina Klaus & Jonathan Newton, 2014. "Stochastic Stability in Assignment Problems," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 14.02, Université de Lausanne, Faculté des HEC, DEEP.
  2. Bettina Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted Stability for Roommate Markets," Working Papers 385, Barcelona Graduate School of Economics.
  3. MAULEON, Ana & ROEHL, Nils & VANNETELBOSCH, Vincent, 2014. "Constitutions and social networks," CORE Discussion Papers 2014003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Newton, Jonathan & Sawa, Ryoji, 2013. "A one-shot deviation principle for stability in matching problems," Working Papers 2013-09, University of Sydney, School of Economics, revised Jul 2014.
  5. Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, vol. 81(C), pages 165-178.
  6. Péter Biró & Gethin Norman, 2013. "Analysis of stochastic matching markets," International Journal of Game Theory, Springer, vol. 42(4), pages 1021-1040, November.
  7. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, University of Paderborn, CIE Center for International Economics.
  8. Boncinelli, Leonardo & Pin, Paolo, 2014. "Efficiency and Stability in a Process of Teams Formation," MPRA Paper 56356, University Library of Munich, Germany.
  9. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers Dissertations 02, University of Paderborn, Faculty of Business Administration and Economics.
  10. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
  11. repec:pdn:wpaper:74 is not listed on IDEAS

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