IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v08y2006i04ns021919890600117x.html
   My bibliography  Save this article

A Note On The Equivalence Of Rationalizability Concepts In Generalized Nice Games

Author

Listed:
  • ALEXANDER ZIMPER

    (School of Economics, Faculty of Commerce, University of Cape Town, Private Bag, Rondebosch, 7701, Cape Town, RSA)

Abstract

Moulin (1984) describes the class of nice games for which the solution concept of point-rationalizability coincides with iterated elimination of strictly 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 ℝ. 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 ofℝnwithn ≥ 2.

Suggested Citation

  • Alexander Zimper, 2006. "A Note On The Equivalence Of Rationalizability Concepts In Generalized Nice Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 669-674.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:04:n:s021919890600117x
    DOI: 10.1142/S021919890600117X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021919890600117X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021919890600117X?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 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. 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. Zimper, Alexander, 2004. "Dominance-Solvable Lattice Games," Sonderforschungsbereich 504 Publications 04-18, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    4. 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.
    5. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
    6. Zimper, Alexander, 2003. "Uniqueness conditions for point-rationalizable solutions of games with metrizable strategy sets," Papers 03-28, Sonderforschungsbreich 504.
    7. 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.
    8. repec:ebl:ecbull:v:3:y:2005:i:7:p:1-6 is not listed on IDEAS
    9. 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.
    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. Roger Guesnerie, 2005. "Strategic Substitutabilities Versus Strategic Complementarities : Towards a General Theory of Expectational Coordination ?," Revue d'économie politique, Dalloz, vol. 115(4), pages 393-412.
    12. Paul Milgrom & John Roberts, 2010. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complements," Levine's Working Paper Archive 449, David K. Levine.
    13. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    14. 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.
    15. George W Evans & Roger Guesnerie & Bruce McGough, 2019. "Eductive Stability in Real Business Cycle Models," Economic Journal, Royal Economic Society, vol. 129(618), pages 821-852.
    16. Roger Guesnerie, 2009. "Macroeconomic and Monetary Policies from the Eductive Viewpoint," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 6, pages 171-202, Central Bank of Chile.
    17. 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.
    18. Ghosal, Sayantan, 2006. "Intertemporal coordination in two-period markets," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 11-35, December.
    19. 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.
    20. Alexandra Belova & Philippe Gagnepain & Stéphane Gauthier, 2020. "An assessment of Nash equilibria in the airline industry," Working Papers halshs-02932780, HAL.
    21. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.

    More about this item

    Keywords

    Rationalizability; dominance solutions; nice games; JEL Classification: C72;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:08:y:2006:i:04:n:s021919890600117x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.