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Fragility of Asymptotic Agreement under Bayesian Learning

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  • Daron Acemoglu
  • Victor Chernozhukov
  • Muhamet Yildiz

Abstract

Under the assumption that individuals know the conditional distributions of signals given the payoff-relevant parameters, existing results conclude that as individuals observe infinitely many signals, their beliefs about the parameters will eventually merge. We first show that these results are fragile when individuals are uncertain about the signal distributions: given any such model, vanishingly small individual uncertainty about the signal distributions can lead to substantial (non-vanishing) differences in asymptotic beliefs. Under a uniform convergence assumption, we then characterize the conditions under which a small amount of uncertainty leads to significant asymptotic disagreement.
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Suggested Citation

  • Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2009. "Fragility of Asymptotic Agreement under Bayesian Learning," Levine's Working Paper Archive 814577000000000139, David K. Levine.
  • Handle: RePEc:cla:levarc:814577000000000139
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    References listed on IDEAS

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    1. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
    2. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    3. Stephen Morris, 1996. "Speculative Investor Behavior and Learning," The Quarterly Journal of Economics, Oxford University Press, vol. 111(4), pages 1111-1133.
    4. Kurz, Mordecai, 1996. "Rational Beliefs and Endogenous Uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 383-397, October.
    5. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
    6. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    7. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    8. Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
    9. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, Oxford University Press, vol. 92(2), pages 323-336.
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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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