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Agreeing to disagree with lexicographic prior beliefs

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  • Bach, Christian W.
  • Perea, Andrés

Abstract

The robustness of Aumann’s seminal agreement theorem with respect to the common prior assumption is considered. More precisely, we show by means of an example that two Bayesian agents with almost identical prior beliefs can agree to completely disagree on their posterior beliefs. Besides, a more detailed agent model is introduced where posterior beliefs are formed on the basis of lexicographic prior beliefs. We then generalize Aumann’s agreement theorem to lexicographic prior beliefs and show that only a slight perturbation of the common lexicographic prior assumption at some–even arbitrarily deep–level is already compatible with common knowledge of completely opposed posterior beliefs. Hence, agents can actually agree to disagree even if there is only a slight deviation from the common prior assumption.

Suggested Citation

  • Bach, Christian W. & Perea, Andrés, 2013. "Agreeing to disagree with lexicographic prior beliefs," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 129-133.
  • Handle: RePEc:eee:matsoc:v:66:y:2013:i:2:p:129-133
    DOI: 10.1016/j.mathsocsci.2013.03.004
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    References listed on IDEAS

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    1. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    2. Giacomo Bonanno & Klaus Nehring, "undated". "Agreeing To Disagree: A Survey," Department of Economics 97-18, California Davis - Department of Economics.
    3. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    4. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    5. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    6. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    7. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    9. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    10. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    11. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    12. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
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    Cited by:

    1. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
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    3. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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