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Refinements of rationalizability for normal-form games

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Author Info
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)

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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.

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Publisher Info
Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 1 ()
Pages: 53-68
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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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Keywords: Rationalizability · refinements;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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.
  2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  3. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October. [Downloadable!] (restricted)
  4. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and common knowledge," Discussion Paper 16, Tilburg University, Center for Economic Research. [Downloadable!]
  5. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August. [Downloadable!] (restricted)
    Other versions:
  6. Vannetelbosch, Vincent J., 1996. "Refinements of Rationalizability for Normal-Form Games: The Main Ideas," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  8. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  10. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November. [Downloadable!] (restricted)
  11. Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  1. Herings, P.J.J. & Mauleon, A. & Vannetelbosch, V.J., 2000. "Social rationalizability," Discussion Paper 81, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
    • Herings,P. Jean-Jacques & Mauleon,Ana & Vannetelbosch,J., 2000. "Social Rationalizability," Research Memoranda 009, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    • Herings,P. Jean-Jacques & Mauleon,Ana & Vannetelbosch,J., 2002. "Social Rationalizability," Research Memoranda 009, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    • J. J. Herings & A. Mauleon & V. Vannetelbosch, 2000. "Social Rationalizability," THEMA Working Papers 2000-36, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
  2. Geir B. Asheim, 2000. "Proper Consistency," Econometric Society World Congress 2000 Contributed Papers 0193, Econometric Society. [Downloadable!]
    Other versions:
  3. Jean-Jacques HERINGS & Ana MAULEON & Vincent J. VANNETELBOSCH, 2000. "Fuzzy Play, Matching Devices and Coordination Failures," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  4. Ana, MAULEON & Vincent, VANNETELBOSCH, 2003. "Farsightedness and Cautiousness in Coalition Formation," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2003003, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2009. "Dynamic Unawareness and Rationalizable Behavior," MPRA Paper 15058, University Library of Munich, Germany. [Downloadable!]
  6. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002. [Downloadable!]
  7. A. Mauleon & V. Vannetelbosch, 2000. "Coalitional Negotiation with Monitoring," THEMA Working Papers 2000-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
  8. Jean-Jacques HERINGS & Ana MAULEON & Vincent J. VANNETELBOSCH, 2001. "Rationalizability for Social Environments," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001028, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  9. Ana MAULEON & Vincent J. VANNETELBOSCH, 2001. "Bargaining with Endogenous Deadlines," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  10. P. Jean-Jacques Herings & Vincent J. Vannetelbosch, 1998. "The Equivalence of the Dekel-Fudenberg Iterative Procedure and Weakly Perfect Rationalizability," Cowles Foundation Discussion Papers 1173, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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