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Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium

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  • Giacomo Bonanno

    (Department of Economics, University of California, Davis, CA 95616-8578, USA)

Abstract

In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (Bonanno, 2016), the notion of PBE was used to provide a characterization of SE in terms of a strengthening of the two defining components of PBE (besides sequential rationality), namely AGM consistency and Bayes consistency. In this paper we explore the gap between PBE and SE by identifying solution concepts that lie strictly between PBE and SE; these solution concepts embody a notion of “conservative” belief revision. Furthermore, we provide a method for determining if a plausibility order on the set of histories is choice measurable, which is a necessary condition for a PBE to be a SE.

Suggested Citation

  • Giacomo Bonanno, 2016. "Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium," Games, MDPI, vol. 7(4), pages 1-23, November.
    • Handle: RePEc:gam:jgames:v:7:y:2016:i:4:p:35-:d:82531
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    References listed on IDEAS

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    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. 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. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
    4. 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.
    5. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    7. 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.
    8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    9. Perea, Andres, 2002. "A note on the one-deviation property in extensive form games," Games and Economic Behavior, Elsevier, vol. 40(2), pages 322-338, August.
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    Cited by:

    1. Gisèle Umbhauer & Arnaud Wolff, 2019. "Individually-Consistent Sequential Equilibrium," Working Papers of BETA 2019-39, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    2. Paul Weirich, 2017. "Epistemic Game Theory and Logic: Introduction," Games, MDPI, vol. 8(2), pages 1-3, March.

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    More about this item

    Keywords

    plausibility order; minimal belief revision; Bayesian updating; independence; sequential equilibrium;
    All these keywords.

    JEL classification:

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

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