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Farsighted Stability for Roommate Markets

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  • Bettina Klaus
  • Flip Klijn
  • Markus Walzl

Abstract

Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set (Examples 1 and 2).

Suggested Citation

  • Bettina Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted Stability for Roommate Markets," Working Papers 385, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:385
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    References listed on IDEAS

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    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 461-471, March.
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    5. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
    6. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    7. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," Working Papers 315, Barcelona School of Economics.
    8. 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.
    9. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    10. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
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    Cited by:

    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. Ana Mauleon & Elena Molis & Vincent Vannetelbosch & Wouter Vergote, 2014. "Dominance invariant one-to-one matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 925-943, November.
    3. Hirata, Daisuke & Kasuya, Yusuke & Tomoeda, Kentaro, 2021. "Stability against robust deviations in the roommate problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 474-498.
    4. Ata Atay & Sylvain Funck & Ana Mauleon & Vincent Vannetelbosch, 2023. "Matching markets with farsighted couples," UB School of Economics Working Papers 2023/445, University of Barcelona School of Economics.
    5. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Working Papers 005-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.
    6. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    7. Gudmundsson , Jens, 2014. "Sequences in Pairing Problems: A New Approach to Reconcile Stability with Strategy-Proofness for Elementary Matching Problems," Working Papers 2014:40, Lund University, Department of Economics.
    8. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    9. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," LIDAM Discussion Papers CORE 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    11. Toshiyuki Hirai, 2018. "Single-payoff farsighted stable sets in strategic games with dominant punishment strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1087-1111, November.
    12. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    13. N. Roketskiy, 2012. "Farsightedly Stable Matchings," Working Papers 12-26, NET Institute.
    14. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    15. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.
    16. Wouter Vergote, 2019. "Revisiting stability in one-to-one matching problems," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 59-75, May.

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    More about this item

    Keywords

    core; farsighted stability; one- and two-sided matching; roommate markets; von Neumann-Morgenstern stability;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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