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Quantum-like model of subjective expected utility

Author

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  • Basieva, Irina
  • Khrennikova, Polina
  • Pothos, Emmanuel M.
  • Asano, Masanari
  • Khrennikov, Andrei
Abstract
We present a very general quantum-like model of lottery selection based on representation of beliefs of an agent by pure quantum states. Subjective probabilities are mathematically realized in the framework of quantum probability (QP). Utility functions are borrowed from the classical decision theory. But in the model they are represented not only by their values. Heuristically one can say that each value ui=u(xi) is surrounded by a cloud of information related to the event (A,xi). An agent processes this information by using the rules of quantum information and QP. This process is very complex; it combines counterfactual reasoning for comparison between preferences for different outcomes of lotteries which are in general complementary. These comparisons induce interference type effects (constructive or destructive). The decision process is mathematically represented by the comparison operator and the outcome of this process is determined by the sign of the value of corresponding quadratic form on the belief state. This operational process can be decomposed into a few subprocesses. Each of them can be formally treated as a comparison of subjective expected utilities and interference factors (the latter express, in particular, risks related to lottery selection). The main aim of this paper is to analyze the mathematical structure of these processes in the most general situation: representation of lotteries by noncommuting operators.

Suggested Citation

  • Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    • Handle: RePEc:eee:mateco:v:78:y:2018:i:c:p:150-162
    DOI: 10.1016/j.jmateco.2018.02.001
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    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Samuelson, Paul A, 1977. "St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described," Journal of Economic Literature, American Economic Association, vol. 15(1), pages 24-55, March.
    3. 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.
    4. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, September.
    5. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    6. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    7. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    8. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    9. Raymond J. Hawkins & B. Roy Frieden, 2012. "Asymmetric Information and Quantization in Financial Economics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, December.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. 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.
    12. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    13. Daniel Kahneman & Richard H. Thaler, 2006. "Anomalies: Utility Maximization and Experienced Utility," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 221-234, Winter.
    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. Emmanuel Haven & Andrei Khrennikov & Terry Robinson, 2017. "Quantum Methods in Social Science:A First Course," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0080, February.
    16. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    17. Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
    18. Haven, Emmanuel & Sozzo, Sandro, 2016. "A generalized probability framework to model economic agents' decisions under uncertainty," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 297-303.
    19. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    20. Masanari Asano & Irina Basieva & Andrei Khrennikov & Masanori Ohya & Yoshiharu Tanaka, 2017. "A Quantum-like Model of Selection Behavior," Papers 1705.08536, arXiv.org.
    21. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    22. 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.
    23. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    24. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    25. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    26. Mark Machina, 2005. "‘Expected utility / subjective probability’ analysis without the sure-thing principle or probabilistic sophistication," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 1-62, July.
    27. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
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    2. Di Salvo, Rosa & Gorgone, Matteo & Oliveri, Francesco, 2020. "Generalized Hamiltonian for a two-mode fermionic model and asymptotic equilibria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Charles-Cadogan, G., 2021. "Utility Representation in Abstract Wiener Space," CRETA Online Discussion Paper Series 70, Centre for Research in Economic Theory and its Applications CRETA.
    4. Jingmei Xiao & Mei Cai & Yu Gao, 2022. "A VIKOR-Based Linguistic Multi-Attribute Group Decision-Making Model in a Quantum Decision Scenario," Mathematics, MDPI, vol. 10(13), pages 1-23, June.
    5. Charles-Cadogan, G., 2018. "Probability interference in expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 163-175.
    6. Eric Ghysels & Jack Morgan, 2024. "On Quantum Ambiguity and Potential Exponential Computational Speed-Ups to Solving Dynamic Asset Pricing Models," Papers 2405.01479, arXiv.org, revised May 2024.
    7. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    8. Charles-Cadogan, G., 2021. "Incoherent Preferences," CRETA Online Discussion Paper Series 69, Centre for Research in Economic Theory and its Applications CRETA.

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