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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

Suggested Citation

  • Ziv Hellman, 2010. "Almost Common Priors," Discussion Paper Series dp560, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp560
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    References listed on IDEAS

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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. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
    3. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    5. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
    6. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    7. 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.
    8. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
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    Cited by:

    1. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    2. Ziv Hellman & Miklós Pintér, 2022. "Charges and bets: a general characterisation of common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 567-587, November.
    3. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Jul 2023.
    4. Bach, Christian W. & Perea, Andrés, 2013. "Agreeing to disagree with lexicographic prior beliefs," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 129-133.
    5. Ziv Hellman & Miklós Pintér, 2020. "Charges and Bets: A General Characterisation of Common Priors," Working Papers 2020-06, Bar-Ilan University, Department of Economics.
    6. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    7. Gizatulina, Alia & Hellman, Ziv, 2019. "No trade and yes trade theorems for heterogeneous priors," Journal of Economic Theory, Elsevier, vol. 182(C), pages 161-184.

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