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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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    Keywords

    Incomplete Information; Informational Robustness; Bayes Correlated Equilibrium; Interim Correlated Rationalizability; Belief-Free Rationalizability;

    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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