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Almost common priors

  • Ziv Hellman

    ()

What happens when priors are not common? We introduce a measure for how far a type space is from having a common prior, which we term prior distance. If a type space has δ prior distance, then for any bet f it cannot be common knowledge that each player expects a positive gain of δ times the sup-norm of 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, can only decrease. We derive an upper bound on the number of refinements needed to arrive at a situation in which the knowledge space has a common prior, which depends only on the number of initial partition elements. Copyright Springer-Verlag 2013

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File URL: http://hdl.handle.net/10.1007/s00182-012-0347-5
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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 42 (2013)
Issue (Month): 2 (May)
Pages: 399-410

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Handle: RePEc:spr:jogath:v:42:y:2013:i:2:p:399-410
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  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. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  4. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
  5. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  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. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
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