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Discounted and Expected Utility from the Probability and Time Trade-Off Model

Author

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  • Salvador Cruz Rambaud

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain
    La Cañada de San Urbano, s/n, 04120 Almería, Spain.)

  • Ana María Sánchez Pérez

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain
    La Cañada de San Urbano, s/n, 04120 Almería, Spain.)

Abstract

This paper shows the interaction between probabilistic and delayed rewards. In decision- making processes, the Expected Utility (EU) model has been employed to assess risky choices whereas the Discounted Utility (DU) model has been applied to intertemporal choices. Despite both models being different, they are based on the same theoretical principle: the rewards are assessed by taking into account the sum of their utilities and some similar anomalies have been revealed in both models. The aim of this paper is to characterize and consider particular cases of the Time Trade-Off (PPT) model and show that they correspond to the EU and DU models. Additionally, we will try to build a PTT model starting from a discounted and an expected utility model able to overcome the limitations pointed out by Baucells and Heukamp.

Suggested Citation

  • Salvador Cruz Rambaud & Ana María Sánchez Pérez, 2020. "Discounted and Expected Utility from the Probability and Time Trade-Off Model," Mathematics, MDPI, vol. 8(4), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:601-:d:345837
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    References listed on IDEAS

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    1. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    2. Keren, Gideon & Roelofsma, Peter, 1995. "Immediacy and Certainty in Intertemporal Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 63(3), pages 287-297, September.
    3. Cruz Rambaud, Salvador & Parra Oller, Isabel María & Valls Martínez, María del Carmen, 2018. "The amount-based deformation of the q-exponential discount function: A joint analysis of delay and magnitude effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 788-796.
    4. Yoram Halevy, 2008. "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect," American Economic Review, American Economic Association, vol. 98(3), pages 1145-1162, June.
    5. Vital Anderhub & Werner Güth & Uri Gneezy & Doron Sonsino, 2001. "On the Interaction of Risk and Time Preferences: An Experimental Study," German Economic Review, Verein für Socialpolitik, vol. 2(3), pages 239-253, August.
    6. Manel Baucells & Franz Heukamp, 2010. "Common ratio using delay," Theory and Decision, Springer, vol. 68(1), pages 149-158, February.
    7. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    8. Takahashi, Taiki, 2007. "A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 637-644.
    9. Caliendo, Frank N. & Findley, T. Scott, 2014. "Discount functions and self-control problems," Economics Letters, Elsevier, vol. 122(3), pages 416-419.
    10. Daniele Pennesi, 2017. "Uncertain discount and hyperbolic preferences," Theory and Decision, Springer, vol. 83(3), pages 315-336, October.
    11. Thomas Epper & Helga Fehr-Duda & Adrian Bruhin, 2011. "Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting," Journal of Risk and Uncertainty, Springer, vol. 43(3), pages 169-203, December.
    12. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
    13. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-563, June.
    14. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.
    15. Mark Schneider, 2016. "Dual Process Utility Theory: A Model of Decisions Under Risk and Over Time," Working Papers 16-23, Chapman University, Economic Science Institute.
    16. Manel Baucells & Franz H. Heukamp, 2012. "Probability and Time Trade-Off," Management Science, INFORMS, vol. 58(4), pages 831-842, April.
    17. Chew, Soo Hong & Epstein, Larry G., 1990. "Nonexpected utility preferences in a temporal framework with an application to consumption-savings behaviour," Journal of Economic Theory, Elsevier, vol. 50(1), pages 54-81, February.
    18. James Andreoni & Charles Sprenger, 2010. "Risk Preferences Are Not Time Preferences: Discounted Expected Utility with a Disproportionate Preference for Certainty," NBER Working Papers 16348, National Bureau of Economic Research, Inc.
    19. James Andreoni & Charles Sprenger, 2012. "Risk Preferences Are Not Time Preferences," American Economic Review, American Economic Association, vol. 102(7), pages 3357-3376, December.
    20. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    21. Abdellaoui, Mohammed & Kemel, Emmanuel & Panin, Amma & Vieider, Ferdinand M., 2019. "Measuring time and risk preferences in an integrated framework," Games and Economic Behavior, Elsevier, vol. 115(C), pages 459-469.
    22. Issler, João Victor & Piqueira, Natalia Scotto, 2000. "Estimating Relative Risk Aversion, the Discount Rate, and the Intertemporal Elasticity of Substitution in Consumption for Brazil Using Three Types of Utility Function," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 20(2), November.
    23. Jonathan W. Leland & Mark Schneider, 2017. "Risk Preference, Time Preference, and Salience Perception," Working Papers 17-16, Chapman University, Economic Science Institute.
    24. Keith Coble & Jayson Lusk, 2010. "At the nexus of risk and time preferences: An experimental investigation," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 67-79, August.
    25. Selçuk Onay & Ayse Öncüler, 2007. "Intertemporal choice under timing risk: An experimental approach," Journal of Risk and Uncertainty, Springer, vol. 34(2), pages 99-121, April.
    26. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    27. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2014. "Time Lotteries, Second Version," PIER Working Paper Archive 15-026v2, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 12 Jan 2018.
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