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Robust implementation in weakly perfect Bayesian strategies

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  • Müller, Christoph

Abstract

We examine a strong form of robust implementation in dynamic mechanisms that is both belief- and belief-revision-free. Specifically, we characterize robust wPBE-implementation, that is, full implementation in weak Perfect Bayesian equilibrium across all type spaces. We introduce a dynamic robust monotonicity condition that is weaker than Bergemann and Morris' (2011) robust monotonicity condition and show that under a conditional no total indifference condition, ex-post incentive compatibility and dynamic robust monotonicity characterize robust wPBE-implementation in general dynamic mechanisms. We also introduce a notion of weakly rationalizable implementation (wr-implementation) and prove that it is equivalent to robust wPBE-implementation. Applied to static mechanisms, wr-implementation exactly characterizes a version of static belief-free implementation.

Suggested Citation

  • Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jetheo:v:189:y:2020:i:c:s0022053120300399
    DOI: 10.1016/j.jet.2020.105038
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    More about this item

    Keywords

    Robust implementation; Dynamic mechanisms; Weak rationalizability; Weak perfect Bayesian equilibrium; Dynamic robust monotonicity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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