IDEAS home Printed from https://ideas.repec.org/p/mnh/spaper/2741.html

A note on the equivalence of rationalizability concepts in generalized nice games

Author

Listed:
  • Zimper, Alexander

Abstract

Moulin (1984) describes the class of nice games for which the solution concept of point-rationalizability coincides with iterated elimination of strongly dominated strategies. As a consequence nice games have the desirable property that all rationalizability concepts determine the same strategic solution. However, nice games are characterized by rather strong assumptions. For example, only single-valued best responses are admitted and the individual strategy sets have to be convex and compact subsets of the real line R1. This note shows that equivalence of all rationalizability concepts can be extended to multi-valued best response correspondences. The surprising finding is that equivalence does not hold for individual strategy sets that are compact and convex subsets of Rn with n≥1.

Suggested Citation

  • Zimper, Alexander, 2004. "A note on the equivalence of rationalizability concepts in generalized nice games," Papers 04-03, Sonderforschungsbreich 504.
    • Handle: RePEc:mnh:spaper:2741
    as

    Download full text from publisher

    File URL: https://madoc.bib.uni-mannheim.de/2741/1/dp04_03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
    3. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    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. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    2. Zimper, Alexander, 2005. "Equivalence between best responses and undominated," Papers 05-08, Sonderforschungsbreich 504.
    3. repec:ebl:ecbull:v:3:y:2005:i:7:p:1-6 is not listed on IDEAS
    4. Zimper, Alexander, 2006. "Uniqueness conditions for strongly point-rationalizable solutions to games with metrizable strategy sets," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 729-751, September.
    5. Zimper, Alexander, 2004. "Dominance-Solvable Lattice Games," Sonderforschungsbereich 504 Publications 04-18, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    6. Zimper, Alexander, 2004. "On the Existence of Strategic Solutions for Games with Security- and Potential Level Players," Sonderforschungsbereich 504 Publications 04-04, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    7. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
    8. Zimper, Alexander, 2003. "Uniqueness conditions for point-rationalizable solutions of games with metrizable strategy sets," Papers 03-28, Sonderforschungsbreich 504.
    9. Alexander Zimper, 2005. "Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-6.
    10. Roger Guesnerie & Pedro Jara-Moroni, 2007. "Expectational coordination in a class of economic models: Strategic substitutabilities versus strategic complementarities," PSE Working Papers halshs-00587837, HAL.
    11. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    12. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2020. "Two-person pairwise solvable games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 385-409, June.
    13. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    14. Roger Guesnerie & Pedro Jara-Moroni, 2011. "Expectational coordination in simple economic contexts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 205-246, June.
    15. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    16. Bao, Te & Duffy, John, 2016. "Adaptive versus eductive learning: Theory and evidence," European Economic Review, Elsevier, vol. 83(C), pages 64-89.
    17. Ayan Bhattacharya, 2022. "Arbitrage from a Bayesian's Perspective," Papers 2211.03244, arXiv.org.
    18. Evans, George W. & Guesnerie, Roger, 2005. "Coordination on saddle-path solutions: the eductive viewpoint--linear multivariate models," Journal of Economic Theory, Elsevier, vol. 124(2), pages 202-229, October.
    19. Alexander Zimper, 2017. "Rationalizable Information Equilibria," Working Papers 201745, University of Pretoria, Department of Economics.
    20. Weinstein, Jonathan & Yildiz, Muhamet, 2011. "Sensitivity of equilibrium behavior to higher-order beliefs in nice games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 288-300, May.
    21. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.

    More about this item

    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:mnh:spaper:2741. 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: Katharina Rautenberg (email available below). General contact details of provider: https://edirc.repec.org/data/sfmande.html .

    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.