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A characterization of sequential equilibrium in terms of AGM belief revision

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  • 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
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    File URL: https://repec.dss.ucdavis.edu/files/4q8KXxTuvi8g8CsvNYzj3gxQ/09-14.pdf
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    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. 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.
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    6. 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.
    7. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
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    9. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
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    Full references (including those not matched with items on IDEAS)

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    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

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