IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v28y1999i1p53-68.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00182/papers/9028001/90280053.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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, December.
    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.
    4. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
    5. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 13-25.
    6. Vannetelbosch, Vincent J., 1996. "Refinements of Rationalizability for Normal-Form Games: The Main Ideas," LIDAM Discussion Papers IRES 1996012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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," Research Memorandum 017, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    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. Vannetelbosch, Vincent J., 1996. "Bargaining with an Endogenous Deadline," LIDAM Discussion Papers IRES 1996011, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    13. Asheim,G.B., 1999. "Proper consistency," Memorandum 31/1999, Oslo University, Department of Economics.
    14. Vincent Vannetelbosch, 1999. "Alternating-Offer Bargaining and Common Knowledge of Rationality," Theory and Decision, Springer, vol. 47(2), pages 111-138, October.
    15. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    16. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    17. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    18. A. Mauleon & V. Vannetelbosch, 2000. "Coalitional Negotiation with Monitoring," THEMA Working Papers 2000-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    19. MAULEON, Ana & VANNETELBOSCH, Vincent, 1999. "Coalitional negotiation," LIDAM Discussion Papers CORE 1999020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jin, Ye & Zhou, Zhen & Brandenburger, Adam, 2023. "Coordination via delay: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 137(C), pages 23-49.
    2. Andreas Blume & Peter H. Kriss & Roberto A. Weber, 2017. "Pre-play communication with forgone costly messages: experimental evidence on forward induction," Experimental Economics, Springer;Economic Science Association, vol. 20(2), pages 368-395, June.
    3. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    4. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    5. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    6. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    7. Geir B. Asheim & Martin Dufwenberg, 2003. "Deductive Reasoning in Extensive Games," Economic Journal, Royal Economic Society, vol. 113(487), pages 305-325, April.
    8. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    9. Vincent Vannetelbosch, 1999. "Alternating-Offer Bargaining and Common Knowledge of Rationality," Theory and Decision, Springer, vol. 47(2), pages 111-138, October.
    10. Blume, Andreas, 1998. "Communication, Risk, and Efficiency in Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 171-202, February.
    11. Vincent P. Crawford, 2016. "New Directions for Modelling Strategic Behavior: Game-Theoretic Models of Communication, Coordination, and Cooperation in Economic Relationships," Journal of Economic Perspectives, American Economic Association, vol. 30(4), pages 131-150, Fall.
    12. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    13. David Sally, 2002. "`What an Ugly Baby!'," Rationality and Society, , vol. 14(1), pages 78-108, February.
    14. Perea Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Filipe Costa Souza & Leandro Chaves Rêgo, 2014. "Mixed Equilibrium, Collaborative Dominance and Burning Money: An Experimental Study," Group Decision and Negotiation, Springer, vol. 23(3), pages 377-400, May.
    16. Cubitt, Robin P. & Sugden, Robert, 2014. "Common Reasoning In Games: A Lewisian Analysis Of Common Knowledge Of Rationality," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 285-329, November.
    17. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    18. Huck, Steffen & Muller, Wieland, 2005. "Burning money and (pseudo) first-mover advantages: an experimental study on forward induction," Games and Economic Behavior, Elsevier, vol. 51(1), pages 109-127, April.
    19. Robin P. Cubitt & Robert Sugden, 2008. "Common reasoning in games," Discussion Papers 2008-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    20. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.

    More about this item

    Keywords

    Rationalizability · refinements;

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:28:y:1999:i:1:p:53-68. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.