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Characterizing the Common Prior Assumption

  • Joseph Y. Halpern

    (Cornell University)

Logical characterizations of the common prior assumption (CPA) are investigated. Two approaches are considered. The first is called frame distinguishability and is similar in spirit to the approaches considered in the economics literature. Results similar to those obtained in the economics literature are proved here as well, namely, that we can distinguish finite spaces that satisfy the CPA from those that do not in terms of disagreements in expectation. However, it is shown that, for the language used here, no formulas can distinguish infinite spaces satisfying the CPA from those that do not. The second approach considered is that of finding a sound and complete axiomatization. Such an axiomatization is provided; again, the key axiom involves disagreements in expectation. The same axiom system is shown to be sound and complete both in the finite and the infinite case. Thus, the two approaches to characterizing the CPA behave quite differently in the case of infinite spaces.

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File URL: http://128.118.178.162/eps/game/papers/0004/0004009.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0004009.

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Length: 12 pages
Date of creation: 22 Nov 2000
Date of revision:
Handle: RePEc:wpa:wuwpga:0004009
Note: Type of Document - PDF; prepared on Unix; pages: 12; figures: included
Contact details of provider: Web page: http://128.118.178.162

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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. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  3. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
  4. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  5. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  6. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  7. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, June.
  8. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  9. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  10. 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.
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