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Characterizing the Common Prior Assumption

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  • Halpern, Joseph Y.

Abstract

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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Suggested Citation

  • Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
  • Handle: RePEc:eee:jetheo:v:106:y:2002:i:2:p:316-355
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    References listed on IDEAS

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    1. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
    2. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
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    4. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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    7. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    8. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    9. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    10. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
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    Cited by:

    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    2. Khan, M. Ali & Sun, Yeneng & Tourky, Rabee & Zhang, Zhixiang, 2008. "Similarity of differential information with subjective prior beliefs," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 1024-1039, September.
    3. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    4. Lipman, Barton L., 2010. "Finite order implications of common priors in infinite models," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 56-70, January.
    5. Halpern, Joseph Y. & Pass, Rafael, 2013. "Conservative belief and rationality," Games and Economic Behavior, Elsevier, vol. 80(C), pages 186-192.
    6. Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
    7. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
    8. Klaus Nehring, 2003. "Common Priors For Like-Minded Agents," Economics Working Papers 0035, Institute for Advanced Study, School of Social Science.
    9. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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