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Almost Common Priors

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  • Ziv Hellman

Abstract

What happens when priors are not common? We show that for each type profile τ over a knowledge space (Ω, Π), where the state space Ω is connected with respect to the partition profile Π, we can associate a value 0 ≤ ε ≤ 1 that we term the prior distance of τ , where ε = 0 if and only if the profile has a common prior. If τ has ε prior distance, then for any bet f amongst the players, it cannot be common knowledge that each player expects a positive gain of ε‖f‖ ∞ , thus extending no betting results under common priors. Furthermore, as more information is obtained and partitions are refined, the prior distance, and thus the extent of common knowledge disagreement, decreases. %Length: 18 pages %File-URL: http://ratio.huji.ac.il/sites/default/files/publications/dp560.pdf

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File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp560R.pdf
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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp560.

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Length: 13 pages
Date of creation: Sep 2010
Date of revision:
Publication status: Forthcoming in International Journal of Game Theory.
Handle: RePEc:huj:dispap:dp560

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  1. Ziv Hellman & Dov Samet, 2010. "How Common Are Common Priors?," Discussion Paper Series dp532, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  3. Dov Samet, 1998. "Quantified beliefs and believed quantities," Game Theory and Information 9805003, EconWPA.
  4. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  5. Dov Samet, 1997. "Common Priors and Separation of Convex Sets," Game Theory and Information 9701002, EconWPA.
  6. 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.
  7. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
  8. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
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Cited by:
  1. Bach, Christian W. & Perea, Andrés, 2013. "Agreeing to disagree with lexicographic prior beliefs," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 129-133.

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