IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v51y2012i1p1-12.html
   My bibliography  Save this article

An indistinguishability result on rationalizability under general preferences

Author

Listed:
  • Yi-Chun Chen
  • Xiao Luo

Abstract

In this paper, we show that, in the class of games where each player’s strategy space is compact Hausdorff and each player’s payoff function is continuous and “concave-like,” rationalizability in a variety of general preference models yields the unique set of outcomes of iterated strict dominance. The result implies that rationalizable strategic behavior in these preference models is observationally indistinguishable from that in the subjective expected utility model, in this class of games. Our indistinguishability result can be applied not only to mixed extensions of finite games, but also to other important applications in economics, for example, the Cournot–oligopoly model. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:51:y:2012:i:1:p:1-12
    DOI: 10.1007/s00199-010-0596-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-010-0596-0
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00199-010-0596-0?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. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    2. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
    3. Martin Dufwenberg & Mark Stegeman, 2002. "Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance," Econometrica, Econometric Society, vol. 70(5), pages 2007-2023, September.
    4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    5. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    6. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    7. Joseph Greenberg & Sudheer Gupta & Xiao Luo, 2009. "Mutually acceptable courses of action," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 91-112, July.
    8. Stephen Morris & Dirk Bergemann, 2007. "Strategic Distinguishability With an Application to Robust Virtual Implementation," Levine's Bibliography 843644000000000149, UCLA Department of Economics.
    9. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    12. 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.
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    15. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    16. Kin Chung Lo, 2000. "Rationalizability and the savage axioms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 727-733.
    17. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    18. Tijmen Daniëls, 2008. "Pure strategy dominance with quasiconcave utility functions," Economics Bulletin, AccessEcon, vol. 3(54), pages 1-8.
    19. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    20. Xiao Luo, 2009. "On the foundation of stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 185-201, August.
    21. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    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. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    2. Minqiang Li, 2014. "On Aumann and Serrano’s economic index of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 415-437, February.
    3. Calford, Evan M., 2021. "Mixed strategies and preference for randomization in games with ambiguity averse agents," Journal of Economic Theory, Elsevier, vol. 197(C).
    4. Stephen Morris & Satoru Takahashi, 2012. "Games in Preference Form and Preference Rationalizability," Working Papers 1420, Princeton University, Department of Economics, Econometric Research Program..
    5. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economics Research Papers 2014-032, Friedrich-Schiller-University Jena.
    6. Bulat Gafarov & Bruno Salcedo, 2015. "Ordinal dominance and risk aversion," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 287-298, October.
    7. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    8. Trost, Michael, 2019. "On the equivalence between iterated application of choice rules and common belief of applying these rules," Games and Economic Behavior, Elsevier, vol. 116(C), pages 1-37.

    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. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    2. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    3. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
    4. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    5. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
    6. Luo, Xiao, 2009. "The foundation of stability in extensive games with perfect information," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 860-868, December.
    7. Luo, Xiao & Ma, Chenghu, 2001. "Stable equilibrium in beliefs in extensive games with perfect information," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1801-1825, November.
    8. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
    10. Thomas Jungbauer & Klaus Ritzberger, 2011. "Strategic games beyond expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 377-398, October.
    11. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    12. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    13. 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.
    14. 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.
    15. Trost, Michael, 2019. "On the equivalence between iterated application of choice rules and common belief of applying these rules," Games and Economic Behavior, Elsevier, vol. 116(C), pages 1-37.
    16. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    17. Ma, Chenghu, 2000. "Uncertainty aversion and rationality in games of perfect information," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 451-482, March.
    18. Jian Yang, 2015. "Game-theoretic Modeling of Players' Ambiguities on External Factors," Papers 1510.06812, arXiv.org, revised Apr 2017.
    19. Jürgen Eichberger & David Kelsey & Burkhard Schipper, 2008. "Granny Versus Game Theorist: Ambiguity in Experimental Games," Theory and Decision, Springer, vol. 64(2), pages 333-362, March.
    20. Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 215-230, May.

    More about this item

    Keywords

    Rationalizability; Iterated dominance; General preferences; C70; D82;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:joecth:v:51:y:2012:i:1:p:1-12. 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.