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Countable Spaces and Common Priors

  • Ziv Hellman

We show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks a common prior but has a common improper prior may or may not have a bounded agreeable bet. The iterated expectations characterisation of the existence of common priors extends almost as is, as a sufficient and necessary condition, from finite spaces to countable spaces, but fails to serve as a characterisation of common improper priors. As a side-benefit of the proofs here, we also obtain a constructive proof of the no betting characterisation in finite spaces.

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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp604.

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Length: 35 pages
Date of creation: Apr 2012
Date of revision:
Publication status: forthcoming in IJGT
Handle: RePEc:huj:dispap:dp604
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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. 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.
  3. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  4. Dov Samet, 1997. "Common Priors and Separation of Convex Sets," Game Theory and Information 9701002, EconWPA.
  5. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  6. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  7. Lehrer, Ehud & Samet, Dov, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
  8. Ziv Hellman & Dov Samet, 2010. "How Common Are Common Priors?," Discussion Paper Series dp532, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  9. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  10. Hellman, Ziv, 2007. "Iterated Expectations, Compact Spaces and Common Priors," MPRA Paper 3794, University Library of Munich, Germany.
  11. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
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