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Iterated Expectations, Compact Spaces, and Common Priors

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  • Ziv Hellman

Abstract

Extending to infinite state spaces that are compact metric spaces a result previously attained by D. Samet solely in the context of finite state spaces, a necessary and suficient 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 Cesaro means of 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 compactness is a necessary condition for some of the results.

Suggested Citation

  • Ziv Hellman, 2009. "Iterated Expectations, Compact Spaces, and Common Priors," Discussion Paper Series dp522, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp522
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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp522.pdf
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    References listed on IDEAS

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

    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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