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Expectation and Variation in Multi-Period Decisions

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  • Itzhak Gilboa

    (Tel Aviv University - Tel Aviv University)

Abstract

Multi-period decisions are decisions which determine an individual's payoffs in several periods in the future. This paper examines the theoretical foundations of the prevalent weighted average assumption. More specifically, we use a multi-period interpretation of the famous Ellsberg paradox in decision under uncertainty to show that in many cases of interest additively-separable functionals (in general) and weighted average ones (in particular) do not seem appropriate for the representation of the decision maker's preferences. We then suggest replacing the sure-thing principle, which may be used to axiomatize a weighted average functional, by a weaker version of it. Using the weakened axiom in Schmeidler's nonadditive measure model (reinterpreted for the multi-period context) yields an axiomatization of a larger class of decision rules which are representable by a weighted average of the utility in each period und the utility variation between each two consecutive periods. The weighted average assumption is a special case of the generalized model, a case in which the decision maker is variation neutral. Similarly, we define and characterize variation aversion and variation liking, and show an example of the economic implications of these properties.

Suggested Citation

  • Itzhak Gilboa, 1989. "Expectation and Variation in Multi-Period Decisions," Post-Print hal-00753240, HAL.
  • Handle: RePEc:hal:journl:hal-00753240
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00753240
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    Cited by:

    1. André Lapied & Olivier Renault, 2012. "An Investigation of Time Consistency for Subjective Discontinued Utility," AMSE Working Papers 1210, Aix-Marseille School of Economics, Marseille, France.
    2. Aloisio Araujo, 2015. "General equilibrium, preferences and financial institutions after the crisis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 217-254, February.
    3. Drazen Prelec & George Loewenstein, 1998. "The Red and the Black: Mental Accounting of Savings and Debt," Marketing Science, INFORMS, vol. 17(1), pages 4-28.
    4. Shalev, Jonathan, 1997. "Loss aversion in a multi-period model," Mathematical Social Sciences, Elsevier, vol. 33(3), pages 203-226, June.
    5. Takao Asano & Hiroyuki Kojima, 2013. "Modularity and Monotonicity of Games," KIER Working Papers 871, Kyoto University, Institute of Economic Research.
    6. Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf & Rodrigo Novinski, 2017. "Optimal sharing with an infinite number of commodities in the presence of optimistic and pessimistic agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 131-157, January.
    7. Araujo, Aloisio & Novinski, Rodrigo & Páscoa, Mário R., 2011. "General equilibrium, wariness and efficient bubbles," Journal of Economic Theory, Elsevier, vol. 146(3), pages 785-811, May.
    8. Takao Asano & Hiroyuki Kojima, 2014. "Modularity and monotonicity of games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 29-46, August.
    9. De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
    10. Jonathan Shalev, 1998. "Loss Aversion in Repeated Games," Game Theory and Information 9802005, EconWPA.
    11. Wakai, Katsutoshi, 2011. "Modeling nonmonotone preferences: The case of utility smoothing," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 213-226, March.
    12. Takao Asano & Hiroyuki Kojima, 2013. "An Axiomatization of Choquet Expected Utility with Cominimum Independence," KIER Working Papers 878, Kyoto University, Institute of Economic Research.
    13. Chateauneuf, Alain & Ventura, Caroline, 2013. "G-continuity, impatience and myopia for Choquet multi-period utilities," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 97-105.
    14. Wakai, Katsutoshi, 2013. "An alternative axiomatization of intertemporal utility smoothing," Economics Letters, Elsevier, vol. 119(2), pages 224-227.
    15. Bastianello, Lorenzo & Chateauneuf, Alain, 2016. "About delay aversion," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 62-77.
    16. Bleichrodt, Han & Gafni, Amiram, 1996. "Time preference, the discounted utility model and health," Journal of Health Economics, Elsevier, vol. 15(1), pages 49-66, February.
    17. Kajii, Atsushi & Kojima, Hiroyuki & Ui, Takashi, 2007. "Cominimum additive operators," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 218-230, February.
    18. André Lapied & Robert Kast, 2005. "Updating Choquet valuation and discounting information arrivals," Working Papers 05-09, LAMETA, Universitiy of Montpellier, revised Jan 2005.
    19. Dan Protopopescu, 2007. "Improving the Risk Concept: A Revision of Arrow-Pratt Theory in the Context of Controlled Dynamic Stochastic Environments," UFAE and IAE Working Papers 727.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 03 Dec 2009.
    20. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
    21. Protopopescu Dan, 2008. "Improving the Effort Concept: A Revision of the Traditional Approach in the Context of Controlled Dynamic Stochastic Environments," UFAE and IAE Working Papers 739.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 03 Dec 2009.
    22. Wakai, Katsutoshi, 2012. "An infinite-horizon model of nonmonotone utility smoothing," Economics Letters, Elsevier, vol. 116(2), pages 170-173.
    23. Takao Asano & Hiroyuki Kojima, 2015. "An axiomatization of Choquet expected utility with cominimum independence," Theory and Decision, Springer, vol. 78(1), pages 117-139, January.
    24. Chateauneuf, Alain & Rebille, Yann, 2004. "Some characterizations of non-additive multi-period models," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 235-250, November.

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