IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v146y2016icp68-70.html
   My bibliography  Save this article

On the IENBR-solvability of two-person finite games

Author

Listed:
  • Iimura, Takuya

Abstract

We show that a two-person finite game is solved by the iterated elimination of never best responses (IENBR) if and only if it is best response acyclic and strongly solvable in the sense of Nash (1951). Thus the rationalizable strategies (Bernheim, 1984; Pearce, 1984) are equivalent to the Nash equilibrium strategies in two-person finite games if and only if the two conditions are met. We prove this for both mixed strategy games and pure strategy games.

Suggested Citation

  • Iimura, Takuya, 2016. "On the IENBR-solvability of two-person finite games," Economics Letters, Elsevier, vol. 146(C), pages 68-70.
    • Handle: RePEc:eee:ecolet:v:146:y:2016:i:c:p:68-70
    DOI: 10.1016/j.econlet.2016.07.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176516302634
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2016.07.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Krzysztof Apt & Sunil Simon, 2015. "A classification of weakly acyclic games," Theory and Decision, Springer, vol. 78(4), pages 501-524, April.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Ambrus, Attila, 2006. "Coalitional Rationalizability," Scholarly Articles 3200266, Harvard University Department of Economics.
    3. Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
    4. Pei, Ting & Takahashi, Satoru, 2019. "Rationalizable strategies in random games," Games and Economic Behavior, Elsevier, vol. 118(C), pages 110-125.
    5. Lawrence Christiano & Husnu Dalgic & Xiaoming Li, 2022. "Modelling the Great Recession as a Bank Panic: Challenges," Economica, London School of Economics and Political Science, vol. 89(S1), pages 200-238, June.
    6. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    7. 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.
    8. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    9. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    10. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    11. Alós-Ferrer, Carlos & Kuzmics, Christoph, 2013. "Hidden symmetries and focal points," Journal of Economic Theory, Elsevier, vol. 148(1), pages 226-258.
    12. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    13. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    14. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    15. Abhijit Banerjee & Jörgen W. Weibull & Ken Binmore, 1996. "Evolution and Rationality: Some Recent Game-Theoretic Results," International Economic Association Series, in: Beth Allen (ed.), Economics in a Changing World, chapter 4, pages 90-117, Palgrave Macmillan.
    16. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    17. Seel, Christian & Tsakas, Elias, 2017. "Rationalizability and Nash equilibria in guessing games," Games and Economic Behavior, Elsevier, vol. 106(C), pages 75-88.
    18. Isogai, Shigeki & Shen, Chaohai, 2023. "Multiproduct firm’s reputation and leniency program in multimarket collusion," Economic Modelling, Elsevier, vol. 125(C).
    19. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2023. "Social Rationalizability with Mediation," Dynamic Games and Applications, Springer, vol. 13(2), pages 440-461, June.
    20. 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.

    More about this item

    Keywords

    Iterated elimination of never best responses; Rationalizable strategies; Best response acyclic games; Strongly solvable games;
    All these keywords.

    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:eee:ecolet:v:146:y:2016:i:c:p:68-70. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.