IDEAS home Printed from https://ideas.repec.org/p/cda/wpaper/33.html
   My bibliography  Save this paper

A characterization of sequential equilibrium in terms of AGM belief revision

Author

Listed:
  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract

In [G. Bonanno, Rational choice and AGM belief revision, Artificial Intelligence, 2009] a semantics for one-stage AGM belief revision was proposed based on choice frames, borrowed from the rational choice literature. In this paper we extend the semantics of choice frames to deal with iterated belief revision and use the corresponding structures to analyze extensive-form games. Choice frames can be used to represent a player's initial beliefs and disposition to change those beliefs when informed that it is her turn to move. If the frame satisfies AGM-consistency and a natural postulate for iterated belief revision, then it is rationalizable by a total pre-order on the set of histories. We show that three properties of this total pre-order, together with the hypothesis of agreement among players, provide a characterization of the notion of consistent assessment, which is the central component of the notion of sequential equilibrium proposed by Kreps and Wilson [Econometrica, 1982].

Suggested Citation

  • Giacomo Bonanno, 2009. "A characterization of sequential equilibrium in terms of AGM belief revision," Working Papers 33, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:33
    as

    Download full text from publisher

    File URL: https://repec.dss.ucdavis.edu/files/4q8KXxTuvi8g8CsvNYzj3gxQ/09-14.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. Bonanno, Giacomo, 1992. "Players' information in extensive games," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 35-48, August.
    3. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Synchronic information, knowledge and common knowledge in extensive games," Research in Economics, Elsevier, vol. 53(1), pages 77-99, March.
    4. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
    5. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
    6. Perea y Monsuwe, Andres & Jansen, Mathijs & Peters, Hans, 1997. "Characterization of Consistent Assessments in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 238-252, October.
    7. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
    8. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    9. Kohlberg, Elon & Reny, Philip J., 1997. "Independence on Relative Probability Spaces and Consistent Assessments in Game Trees," Journal of Economic Theory, Elsevier, vol. 75(2), pages 280-313, August.
    10. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
    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. Giacomo Bonanno, 2009. "A characterization of sequential equilibrium in terms of AGM belief revision," Working Papers 914, University of California, Davis, Department of Economics.
    2. Giacomo Bonanno, 2013. "AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 567-592, August.
    3. Giacomo Bonanno, 2011. "Perfect Bayesian equilibrium. Part II: epistemic foundations," Working Papers 111, University of California, Davis, Department of Economics.
    4. Giacomo Bonanno, 2011. "Perfect Bayesian equilibrium. Part II: epistemic foundations," Working Papers 302, University of California, Davis, Department of Economics.
    5. Giacomo Bonanno, 2013. "AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 567-592, August.
    6. Carlos Pimienta, 2011. "Weakly-Bayesian and Consistent Assessments," Discussion Papers 2012-02, School of Economics, The University of New South Wales.
    7. Carlos Pimienta, 2014. "Bayesian and consistent assessments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 601-617, April.
    8. Giacomo Bonanno, 2016. "Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium," Games, MDPI, vol. 7(4), pages 1-23, November.
    9. Streufert, Peter A., 2015. "An elementary proof that additive i-likelihood characterizes the supports of consistent assessments," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 37-46.
    10. Giacomo Bonanno, 2016. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1071-1094, November.
    11. Burkhard Schipper, 2014. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," Working Papers 83, University of California, Davis, Department of Economics.
    12. Giacomo Bonanno, 2016. "Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-23, November.
    13. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    14. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. Balkenborg Dieter & Kuzmics Christoph & Hofbauer Josef, 2019. "The Refined Best Reply Correspondence and Backward Induction," German Economic Review, De Gruyter, vol. 20(1), pages 52-66, February.
    16. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    17. Peter A. Streufert, 2006. "Characterizing Consistency by Monomials and by Product Dispersions," University of Western Ontario, Departmental Research Report Series 20062, University of Western Ontario, Department of Economics.
    18. Pierpaolo Battigalli & Nicolò Generoso, 2021. "Information Flows and Memory in Games," Working Papers 678, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    19. Hanjoon Michael Jung, 2020. "Perfect regular equilibrium," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(4), pages 380-398, December.
    20. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.

    More about this item

    Keywords

    Choice function; AGM belief revision; extensive-form game; sequential equilibrium; iterated belief revision; backward induction.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    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:cda:wpaper:33. 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: Letters and Science IT Services Unit (email available below). General contact details of provider: https://edirc.repec.org/data/educdus.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.