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Refinements of rationalizability for normal-form games

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Author Info
Herings, P.J.J.
Vannetelbosch, V.J. (Tilburg University, Center for Economic Research)

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Abstract

In normal-form games, rationalizability (Bernheim [3], Pearce [11]) on its own fails to exclude some very implausible strategy choices. Three main refinements of rationalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate unreasonable outcomes and suffer from several drawbacks. Therefore, we introduce the trembling-hand rationalizability concept, where the players' actions have to be best responses also against perturbed conjectures. We also propose another refinement: weakly perfect rationalizability, where players' actions that are not best responses are only played with a very small probability. We show the relationship between perfect rationalizability and weakly perfect rationalizability as well as the relationship between proper rationalizability and weakly perfect rationalizability : weakly perfect rationalizability is a weaker refinement than both perfect and proper rationalizability. Moreover, in two-player games it holds that weakly perfect rationalizability is a weaker refinement than trembling-hand rationalizability. The other relationships between the various refinements are illustrated by means of examples. For the relationship between any other two refinements we give examples showing that the remaining set of strategies corresponding to the first refinement can be either smaller or larger than the one corresponding to the second refinement.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 3.

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Date of creation: 1997
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Handle: RePEc:dgr:kubcen:19973

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  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)
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  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!]
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    • 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!]
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  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!]
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  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!]
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  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!]
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  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!]
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  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!]
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