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Bayesian Updating for Complementarily Additive Beliefs under Ambiguity

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  • Mayumi Horie

    () (Hiroshima University of Economics)

Abstract

This paper proposes a formal characterization of extended Bayesian updating for complementarily additive subjective beliefs under ambiguity, which are compatible with a wide range of choice behavior toward ambiguity. The main result shows that, based on the biseparability of Ghirardato and Marinacci (2001), extended Bayesian updating characterizes the update rule which is a step-by-step composite updating for priors, where one of Dempster-Shafer rule, Bayes'update rule and Fagin-Halpern rule is applied to each step. As applications, more speci c preference relations are examined, such as the maxmin expected utility, the rank-dependent expected utility, and the concave expected utility preferences by Lehrer (2009).

Suggested Citation

  • Mayumi Horie, 2016. "Bayesian Updating for Complementarily Additive Beliefs under Ambiguity," KIER Working Papers 935, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:935
    as

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP935.pdf
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    References listed on IDEAS

    as
    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    3. Grant, Simon & Kajii, Atsushi & Polak, Ben, 2000. "Decomposable Choice under Uncertainty," Journal of Economic Theory, Elsevier, vol. 92(2), pages 169-197, June.
    4. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    5. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Hanany, Eran & Klibanoff, Peter, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    7. Mayumi Horie, 2007. "A General Update Rule for Convex Capacities," KIER Working Papers 644, Kyoto University, Institute of Economic Research.
    8. Gul, Faruk & Pesendorfer, Wolfgang, 2015. "Hurwicz expected utility and subjective sources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 465-488.
    9. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.
    10. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    11. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. Hong Chew Soo & Epstein Larry G. & Wakker Peter, 1993. "A Unifying Approach to Axiomatic Non-expected Utility Theories: Correction and Comment," Journal of Economic Theory, Elsevier, vol. 59(1), pages 183-188, February.
    14. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
    15. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    16. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    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. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May.
    19. Chew, S. H. & Epstein, L. G., 1989. "A unifying approach to axiomatic non-expected utility theories," Journal of Economic Theory, Elsevier, vol. 49(2), pages 207-240, December.
    20. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
    21. Alon, Shiri & Schmeidler, David, 2014. "Purely subjective Maxmin Expected Utility," Journal of Economic Theory, Elsevier, vol. 152(C), pages 382-412.
    22. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    23. 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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    More about this item

    Keywords

    ambiguous belief; Bayesian update rule; multiple priors; non-additive measure; subjective probability; biseparable preference;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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