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Refinements of rationalizability for normal-form games

Author

Listed:
  • Vincent J. Vannetelbosch

    (CORE, University of Louvain, voie du Roman Pays 34, B-1348 Louvain-la-Neuve, Belgium)

  • P. Jean-Jacques Herings

    (CentER and Department of Econometrics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

Abstract

There exist three equivalent definitions of perfect Nash equilibria which differ in the way "best responses against small perturbations" are defined. It is shown that applying the spirit of these definitions to rationalizability leads to three different refinements of rationalizable strategies which are termed perfect (Bernheim, 1984), weakly perfect and trembling-hand perfect rationalizability, respectively. We prove that weakly perfect rationalizability is weaker than both perfect and proper (Schuhmacher, 1995) rationalizability and in two-player games it is weaker than trembling-hand perfect rationalizability. By means of examples, it is shown that no other relationships can be found.

Suggested Citation

  • Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 1999. "Refinements of rationalizability for normal-form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 53-68.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:1:p:53-68
    Note: Received: January 1997/final version: August 1998
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    References listed on IDEAS

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    1. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384.
    3. Ben-Porath, Elchanan & Dekel, Eddie, 1992. "Signaling future actions and the potential for sacrifice," Journal of Economic Theory, Elsevier, vol. 57(1), pages 36-51.
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    Citations

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    Cited by:

    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    2. P. Jean-Jacques Herings & Ana Mauleon & Vincent J. Vannetelbosch, 2004. "Fuzzy play, matching devices and coordination failures," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 519-531, August.
    3. Kool, C.J.M. & Thornton, D., 2000. "The expectations theory and the founding of the fed: another look at the evidence," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 677-687.
    5. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent J., 2004. "Rationalizability for social environments," Games and Economic Behavior, Elsevier, vol. 49(1), pages 135-156, October.
    6. Mauleon, Ana & Vannetelbosch, Vincent, 2004. "Bargaining with endogenous deadlines," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 321-335, July.
    7. Ana Mauleon & Vincent Vannetelbosch, 2003. "Farsightedness and Cautiousness in Coalition Formation," Working Papers 2003.52, Fondazione Eni Enrico Mattei.
    8. Herings, P.J.J. & Mauleon, A. & Vannetelbosch, V., 2000. "Social Rationalizability," Discussion Paper 2000-81, Tilburg University, Center for Economic Research.
    9. Goossens, J.H.M. & van Hoesel, C.P.M. & Kroon, L.G., 2002. "On solving multi-type line planning problems," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    11. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2017. "Strongly rational sets for normal-form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 35-46, April.
    12. Asheim,G.B., 1999. "Proper consistency," Memorandum 31/1999, Oslo University, Department of Economics.
    13. Vincent Vannetelbosch, 1999. "Alternating-Offer Bargaining and Common Knowledge of Rationality," Theory and Decision, Springer, vol. 47(2), pages 111-138, October.
    14. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    15. A. Mauleon & V. Vannetelbosch, 2000. "Coalitional Negotiation with Monitoring," THEMA Working Papers 2000-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    16. MAULEON, Ana & VANNETELBOSCH, Vincent, 1999. "Coalitional negotiation," LIDAM Discussion Papers CORE 1999020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    Rationalizability · refinements;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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