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Belief-Free Rationalizability and Informational Robustness

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Abstract

We propose an incomplete information analogue of rationalizability. An action is said to be belief-free rationalizable if it survives the following iterated deletion process. At each stage, we delete actions for a type of a player that are not a best response to some conjecture that puts weight only on profiles of types of other players and states that that type thinks possible, combined with actions of those types that have survived so far. We describe a number of applications. This solution concept characterizes the implications of equilibrium when a player is known to have some private information but may have additional information. It thus answers the "informational robustness" question of what can we say about the set of outcomes that may arise in equilibrium of a Bayesian game if players may observe some additional information.

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  • Dirk Bergemann & Stephen Morris, 2016. "Belief-Free Rationalizability and Informational Robustness," Cowles Foundation Discussion Papers 2066, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2066
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    Cited by:

    1. Takashi Ui & Stephen Morris, 2020. "Incomplete Information Robustness," Working Papers on Central Bank Communication 019, University of Tokyo, Graduate School of Economics.
    2. Kivinen, Steven, 2023. "On the manipulability of equitable voting rules," Games and Economic Behavior, Elsevier, vol. 141(C), pages 286-302.
    3. George-Marios Angeletos & Karthik A. Sastry, 2018. "Managing Expectations: Instruments vs. Targets," NBER Working Papers 25404, National Bureau of Economic Research, Inc.
    4. R Jain & M Lombardi, 2021. "On the Relationship between Robust and Rationalizable Implementation," IEAS Working Paper : academic research 21-A004, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    5. Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    6. Jaeok Park & Doo Hyung Yun, 2023. "Possibilistic beliefs in strategic games," Theory and Decision, Springer, vol. 95(2), pages 205-228, August.
    7. Ziegler, Gabriel, 2022. "Informational robustness of common belief in rationality," Games and Economic Behavior, Elsevier, vol. 132(C), pages 592-597.

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    More about this item

    Keywords

    Incomplete Information; Informational Robustness; Bayes Correlated Equilibrium; Interim Correlated Rationalizability; Belief-Free Rationalizability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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