IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v8y2020i1d10.1007_s40505-019-00169-1.html
   My bibliography  Save this article

Best-reply sets

Author

Listed:
  • Jonathan Weinstein

    (Washington University in St. Louis)

Abstract

We provide results concerning, in a given normal-form game, which sets of actions are best replies to some belief. Proposition 1 states that for any set S of actions, there is a belief under which all actions in S are simultaneously best replies if and only if no mixture of actions in S is strictly dominated. Similarly, Proposition 2 states that for any set S of actions, there is a full-support belief under which all actions in S are best replies if and only if no mixture of actions in S is weakly dominated. One important consequence is Corollary 1: a two-player game has a totally mixed Nash equilibrium if and only if neither player has a pair of mixed strategies such that one weakly dominates the other.

Suggested Citation

  • Jonathan Weinstein, 2020. "Best-reply sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 105-112, April.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00169-1
    DOI: 10.1007/s40505-019-00169-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-019-00169-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-019-00169-1?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. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    2. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    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. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    2. Michael Trost, 2013. "Epistemic characterizations of iterated deletion of inferior strategy profiles in preference-based type spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 755-776, August.
    3. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
    4. 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.
    5. 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.
    6. Ryan Chahrour & Gaetano Gaballo, 2015. "On the Nature and Stability of Sentiments," Boston College Working Papers in Economics 873, Boston College Department of Economics, revised 05 May 2015.
    7. Segal, Uzi & Sobel, Joel, 2007. "Tit for tat: Foundations of preferences for reciprocity in strategic settings," Journal of Economic Theory, Elsevier, vol. 136(1), pages 197-216, September.
    8. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics.
    9. Hillas, John & Samet, Dov, 2022. "Non-Bayesian correlated equilibrium as an expression of non-Bayesian rationality," Games and Economic Behavior, Elsevier, vol. 135(C), pages 1-15.
    10. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    11. Ben-Porath, Elchanan, 1992. "Rationality, Nash Equilibrium and Backward Induction in Perfect Information Games," Foerder Institute for Economic Research Working Papers 275567, Tel-Aviv University > Foerder Institute for Economic Research.
    12. Adam Brandenburger & Amanda Friedenberg, 2014. "Intrinsic Correlation in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 4, pages 59-111, World Scientific Publishing Co. Pte. Ltd..
    13. Christian Bach & Jérémie Cabessa, 2012. "Common knowledge and limit knowledge," Theory and Decision, Springer, vol. 73(3), pages 423-440, September.
    14. Morris, Stephen & Skiadas, Costis, 2000. "Rationalizable Trade," Games and Economic Behavior, Elsevier, vol. 31(2), pages 311-323, May.
    15. R. J. Aumann & J. H. Dreze, 2005. "When All is Said and Done, How Should You Play and What Should You Expect?," Discussion Paper Series dp387, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    16. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
    17. Lorenzo Bastianello & Mehmet S. Ismail, 2022. "Rationality and correctness in n-player games," Papers 2209.09847, arXiv.org, revised Dec 2023.
    18. 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.
    19. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    20. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.

    More about this item

    Keywords

    Game theory; Normal-form games; Best replies; Rationalizability;
    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:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00169-1. 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.