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Optimal Learning and Ellsberg's Urns

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  • Larry G. Epstein
  • Shaolin Ji

Abstract

We consider the dynamics of learning under ambiguity when learning is costly and is chosen optimally. The setting is Ellsberg's two-urn thought experiment modified by allowing the agent to postpone her choice between bets so that she can learn about the composition of the ambiguous urn. Signals are modeled by a diffusion process whose drift is equal to the true bias of the ambiguous urn and they are observed at a constant cost per unit time. The resulting optimal stopping problem is solved and the effect of ambiguity on the extent of learning is determined. It is shown that rejection of learning opportunities can be optimal for an ambiguity averse agent even given a small cost.

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  • Larry G. Epstein & Shaolin Ji, 2017. "Optimal Learning and Ellsberg's Urns," Papers 1708.01890, arXiv.org.
  • Handle: RePEc:arx:papers:1708.01890
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    References listed on IDEAS

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    1. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
    2. Drew Fudenberg & Philipp Strack & Tomasz Strzalecki, 2015. "Speed, Accuracy, and the Optimal Timing of Choices," Working Paper 254346, Harvard University OpenScholar.
    3. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    4. Milica Milosavljevic & Jonathan Malmaud & Alexander Huth & Christof Koch & Antonio Rangel, 2010. "The Drift Diffusion Model can account for the accuracy and reaction time of value-based choices under high and low time pressure," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 5(6), pages 437-449, October.
    5. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    6. Trautmann, Stefan T. & Zeckhauser, Richard J., 2013. "Shunning uncertainty: The neglect of learning opportunities," Games and Economic Behavior, Elsevier, vol. 79(C), pages 44-55.
    7. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
    8. Butler, Jeff & Guiso, Luigi & Jappelli, Tullio, 2013. "Manipulating Reliance on Intuition Reduces Risk and Ambiguity Aversion," CEPR Discussion Papers 9461, C.E.P.R. Discussion Papers.
    9. Jeffrey Butler & Luigi Guiso & Tullio Jappelli, 2014. "The role of intuition and reasoning in driving aversion to risk and ambiguity," Theory and Decision, Springer, vol. 77(4), pages 455-484, December.
    10. Costis Skiadas, 2013. "Smooth Ambiguity Aversion toward Small Risks and Continuous-Time Recursive Utility," Journal of Political Economy, University of Chicago Press, vol. 121(4), pages 000.
    11. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 97-115, April.
    12. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    13. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    14. Gilboa, Itzhak & Schmeidler, David, 1986. "Maxmin Expected Utility with a Non-Unique Prior," Foerder Institute for Economic Research Working Papers 275405, Tel-Aviv University > Foerder Institute for Economic Research.
    15. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
    16. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    18. Ariel Rubinstein, 2016. "A Typology of Players: Between Instinctive and Contemplative," The Quarterly Journal of Economics, Oxford University Press, vol. 131(2), pages 859-890.
    19. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    20. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: Response Times Study," Levine's Bibliography 321307000000001011, UCLA Department of Economics.
    21. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "Erratum to: The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 117-117, April.
    22. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
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    Cited by:

    1. Roxane Bricet, 2018. "The price for instrumentally valuable information," THEMA Working Papers 2018-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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