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Iterated Expectations, Compact Spaces and Common Priors

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  • Hellman, Ziv

Abstract

Extending to infinite state spaces that are compact metric spaces a result previously attained by Dov Samet solely in the context of finite state spaces, a necessary and sufficient condition for the existence of a common prior for several players is given in terms of the players’ present beliefs only. A common prior exists if and only if for each random variable it is common knowledge that all its iterated expectations with respect to any permutation converge to the same value; this value is its expectation with respect to the common prior. It is further shown that the restriction to compact metric spaces is ‘natural’ when semantic type spaces are derived from syntactic models, and that compactness is a necessary condition. Many proofs are based on results from the theory of Markov chains.

Suggested Citation

  • Hellman, Ziv, 2007. "Iterated Expectations, Compact Spaces and Common Priors," MPRA Paper 3794, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3794
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    References listed on IDEAS

    as
    1. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    2. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
    3. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    4. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    5. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    6. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    7. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
    8. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    9. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
    10. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
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    Citations

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    Cited by:

    1. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    2. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.

    More about this item

    Keywords

    common priors; Markov chains; type spaces; iterated expectations;

    JEL classification:

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

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