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The context of the game

Author

Listed:
  • Amanda Friedenberg

    () (Arizona State University)

  • Martin Meier

    () (Institut für Höhere Studien)

Abstract

Abstract We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t change the analysis—i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.

Suggested Citation

  • Amanda Friedenberg & Martin Meier, 2017. "The context of the game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 347-386, February.
  • Handle: RePEc:spr:joecth:v:63:y:2017:i:2:d:10.1007_s00199-015-0938-z
    DOI: 10.1007/s00199-015-0938-z
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    References listed on IDEAS

    as
    1. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    2. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    3. Battigalli, Pierpaolo & Friedenberg, Amanda, 2012. "Forward induction reasoning revisited," Theoretical Economics, Econometric Society, vol. 7(1), January.
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    6. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
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    More about this item

    Keywords

    Bayesian games; Universal type structure; Robustness; Hierarchies of beliefs; Context;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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