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Von Neumann-Morgenstern farsightedly stable sets in two-sided matching

Author

Listed:
  • MAULEON, Ana
  • VANNETELBOSCH, Vincent J.
  • VERGOTE, Wouter

Abstract

We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict with matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets : a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the von Neumann-Morgenstern (myopically) stable sets, von Neumann-Morgenstern farsightedly stable sets cannot include matchings thar are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences.
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Suggested Citation

  • MAULEON, Ana & VANNETELBOSCH, Vincent J. & VERGOTE, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers RP 2337, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:2337
    Note: In : Theoretical Economics, 6(3), 499-521, 2011
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    File URL: http://dx.doi.org/10.3982/TE527
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    References listed on IDEAS

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    1. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, May.
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    7. 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.
    8. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    9. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    10. 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.
    11. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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    Citations

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    Cited by:

    1. Dutta, Bhaskar & Vohra, Rajiv, 2017. "Rational expectations and farsighted stability," Theoretical Economics, Econometric Society, vol. 12(3), September.
    2. 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.
    3. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.
    4. Carayol, Nicolas & Delille, Rémy & Vannetelbosch, Vincent, 2015. "Allocating value among farsighted players in network formation," Economics Letters, Elsevier, vol. 137(C), pages 50-53.
    5. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.
    6. 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.
    7. Dutta, Bhaskar & Vartiainen, Hannu, 2017. "Coalition Formation and History Dependence," CRETA Online Discussion Paper Series 33, Centre for Research in Economic Theory and its Applications CRETA.
    8. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    9. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," CORE Discussion Papers 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Francis Bloch & Anne van den Nouweland, 2017. "Farsighted Stability with Heterogeneous Expectations," Working Papers 2017.31, Fondazione Eni Enrico Mattei.
    11. Hannu Vartiainen, 2015. "Dynamic stable set as a tournament solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 309-327, September.
    12. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    13. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.
    14. Herings, P.J.J. & Mauleon, A. & Vannetelbosch, V., 2014. "Stability of networks under level-k farsightedness," Research Memorandum 030, Maastricht University, Graduate School of Business and Economics (GSBE).
    15. Anindya Bhattacharya & Victoria Brosi, 2011. "An existence result for farsighted stable sets of games in characteristic function form," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 393-401, May.

    More about this item

    JEL classification:

    • 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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