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Robust α-maxmin representations

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  • Chateauneuf, Alain
  • Qu, Xiangyu
  • Ventura, Caroline
  • Vergopoulos, Vassili

Abstract

The class of α-maxmin representations of an agent’s preferences is meant to achieve a separation between the ambiguity he perceives and his attitude toward this perceived ambiguity. Yet the same preferences may admit a multiplicity of α-maxmin representations that contradict each other. We say that an α-maxmin representation is robust when no other α-maxmin representation exists for the same preferences. We obtain a full characterization of robustness for maxmin representation. In the case of general α-maxmin representations, we obtain sufficient conditions for both robustness and non-robustness. This contributes to better identification of the α-maxmin representations that admit a robust interpretation in terms of perceived ambiguity and ambiguity attitudes.

Suggested Citation

  • Chateauneuf, Alain & Qu, Xiangyu & Ventura, Caroline & Vergopoulos, Vassili, 2024. "Robust α-maxmin representations," Journal of Mathematical Economics, Elsevier, vol. 114(C).
  • Handle: RePEc:eee:mateco:v:114:y:2024:i:c:s0304406824001058
    DOI: 10.1016/j.jmateco.2024.103045
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    References listed on IDEAS

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    1. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    2. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    3. Alain Chateauneuf & Caroline Ventura & Vassili Vergopoulos, 2020. "A Simple Characterization of the Hurwicz Criterium under Uncertainty," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 331-336.
    4. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    5. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2022. "Objective rationality foundations for (dynamic) α-MEU," Journal of Economic Theory, Elsevier, vol. 200(C).
    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    7. Alan Rogers & Matthew Ryan, 2012. "Additivity and Uncertainty," Economics Bulletin, AccessEcon, vol. 32(3), pages 1858-1864.
    8. Beissner, Patrick & Werner, Jan, 2023. "Optimal allocations with α-MaxMin utilities, Choquet expected utilities, and Prospect Theory," Theoretical Economics, Econometric Society, vol. 18(3), July.
    9. Hartmann, Lorenz, 2023. "Strength of preference over complementary pairs axiomatizes alpha-MEU preferences," Journal of Economic Theory, Elsevier, vol. 213(C).
    10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    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. Ghirardato, Paolo & Klibanoff, Peter & Marinacci, Massimo, 1998. "Additivity with multiple priors," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 405-420, November.
    13. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
    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.
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