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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3794.

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Date of creation: 07 Jun 2007
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Handle: RePEc:pra:mprapa:3794

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

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  1. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
  2. Paul Milgrom & Nancy L.Stokey, 1979. "Information, Trade, and Common Knowledge," Discussion Papers 377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer, vol. 28(3), pages 409-434.
  4. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
  5. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  6. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  7. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
  8. Dov Samet, 1997. "Common Priors and Separation of Convex Sets," Game Theory and Information 9701002, EconWPA.
  9. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  10. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
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Cited by:
  1. Ziv Hellman, 2012. "Countable Spaces and Common Priors," Discussion Paper Series dp604, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.

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