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Decision-making with partial information

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  • Eichberger, Jürgen
  • Pasichnichenko, Illia

Abstract

In this paper, we study choice under uncertainty with belief functions. Belief functions can capture partial information by describing what is objectively known about the probabilities of events. State-contingent acts together with a belief function over states induce belief functions over outcomes. We assume that decision makers have preferences over belief functions that reflect both their valuation of outcomes and the information available about the likelihood of outcomes. We provide axioms characterizing a preference representation for belief functions that captures what is (objectively) known about the likelihood of outcomes and combines it with subjective beliefs according to the “principle of insufficient reason” whenever the likelihood of events is unknown. This treatment of partial information yields a natural distinction between ambiguity and ambiguity attitudes. The approach is novel in its treatment of partial information and in its axiomatization of the uniform distribution in case of ignorance.

Suggested Citation

  • Eichberger, Jürgen & Pasichnichenko, Illia, 2021. "Decision-making with partial information," Journal of Economic Theory, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:jetheo:v:198:y:2021:i:c:s0022053121001861
    DOI: 10.1016/j.jet.2021.105369
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    1. Ke, Shaowei, 2019. "Boundedly rational backward induction," Theoretical Economics, Econometric Society, vol. 14(1), January.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    4. Raphaël Giraud & Jean-Marc Tallon, 2011. "Are beliefs a matter of taste? A case for objective imprecise information," Theory and Decision, Springer, vol. 71(1), pages 23-31, July.
    5. Gajdos, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Representation and aggregation of preferences under uncertainty," Journal of Economic Theory, Elsevier, vol. 141(1), pages 68-99, July.
    6. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    7. Klaus Nehring, 2006. "Is it Possible to Define Subjective Probabilities in Purely Behavioral Terms? A Comment on Epstein-Zhang (2001)," Economics Working Papers 0067, Institute for Advanced Study, School of Social Science.
    8. Aurélien Baillon & Zhenxing Huang & Asli Selim & Peter P. Wakker, 2018. "Measuring Ambiguity Attitudes for All (Natural) Events," Econometrica, Econometric Society, vol. 86(5), pages 1839-1858, September.
    9. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    11. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    12. Hans-Werner Sinn, 1980. "A Rehabilitation of the Principle of Insufficient Reason," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 94(3), pages 493-506.
    13. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, December.
    14. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    15. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    16. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    17. William Neilson, 2010. "A simplified axiomatic approach to ambiguity aversion," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 113-124, October.
    18. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    19. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
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    Cited by:

    1. Ani Guerdjikova & Jürgen Eichberger, 2023. "Cases and States ," Working Papers hal-03962412, HAL.
    2. Kops, Christopher & Pasichnichenko, Illia, 2023. "Testing negative value of information and ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 213(C).

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    More about this item

    Keywords

    Principle of insufficient reason; Ambiguity; Ambiguity attitude; Information about events; Belief functions;
    All these keywords.

    JEL classification:

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

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