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A simplified approach to subjective expected utility

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  • Stanca, Lorenzo

Abstract

I provide a novel simplified approach to Savage’s theory of subjective expected utility. Such an approach is based on abstract integral representation theorems in the space of measurable functions. The advantage of such an approach is that these results can be used to easily obtain variations on Savage’s theorem, such as representations with state-dependent utility or probability measures that can have atoms. Finally, I discuss how such an approach can be used in other settings such as decision making under ambiguity.

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  • Stanca, Lorenzo, 2020. "A simplified approach to subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 151-160.
    • Handle: RePEc:eee:mateco:v:87:y:2020:i:c:p:151-160
    DOI: 10.1016/j.jmateco.2020.01.007
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    1. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
    2. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    3. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    4. Castagnoli, Erio & LiCalzi, Marco, 2006. "Benchmarking real-valued acts," Games and Economic Behavior, Elsevier, vol. 57(2), pages 236-253, November.
    5. Mackenzie, Andrew, 2019. "A foundation for probabilistic beliefs with or without atoms," Theoretical Economics, Econometric Society, vol. 14(2), May.
    6. Tomasz Strzalecki, 2013. "Temporal Resolution of Uncertainty and Recursive Models of Ambiguity Aversion," Econometrica, Econometric Society, vol. 81(3), pages 1039-1074, May.
    7. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    8. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    9. Simon Grant & Ben Polak & Tomasz Strzalecki, "undated". "Second-Order Expected Utility," Working Paper 8340, Harvard University OpenScholar.
    10. Ha-Huy, Thai, 2019. "Savage's theorem with atoms," MPRA Paper 96108, University Library of Munich, Germany.
    11. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. 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.
    14. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    15. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    16. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    17. Peter Wakker, 1993. "Unbounded Utility for Savage's “Foundations of Statistics,” and Other Models," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 446-485, May.
    18. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    19. William Neilson, 2010. "A simplified axiomatic approach to ambiguity aversion," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 113-124, October.
    20. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
    21. Peter P. Wakker & Horst Zank, 1999. "State Dependent Expected Utility for Savage's State Space," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 8-34, February.
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    2. Edoardo Berton & Alessandro Doldi & Marco Maggis, 2024. "On conditioning and consistency for nonlinear functionals," Papers 2401.09054, arXiv.org, revised May 2024.
    3. Klibanoff, Peter & Mukerji, Sujoy & Seo, Kyoungwon & Stanca, Lorenzo, 2022. "Foundations of ambiguity models under symmetry: α-MEU and smooth ambiguity," Journal of Economic Theory, Elsevier, vol. 199(C).
    4. Lécuyer, Emy & Riedel, Frank & Stanca, Lorenzo, 2024. "Arbitrage Pricing in Convex, Cash-Additive Markets," Center for Mathematical Economics Working Papers 694, Center for Mathematical Economics, Bielefeld University.

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