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G-continuity, impatience and myopia for Choquet multi-period utilities

Author

Listed:
  • Alain Chateauneuf

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Caroline Ventura

    (PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract
A main goal of this paper is to try to clarify the notions of impatience and myopia, often considered as synonymous in the literature. The occurrence of asset price bubbles (see Araujo et al., 2011) when only myopia is required, explains why we focused on a stronger notion that we define as impatience and which allows to avoid such market anomalies. The first part characterizes the impatience and the myopia in the context of discrete and continuous time flows of income (consumption) valued through a Choquet integral with respect to an (exact) capacity. Our results unlike the additive utility functional allow to disentangle myopia from impatience: impatience requires myopia but the converse is false. Moreover it turns out that in our framework a decision maker exhibits more easily impatience and myopia in continuous time than in discrete time. In the second part, we recall the generalization given by Rébillé (2008) of the Yosida-Hewitt decomposition of an additive set function into a continuous part and a pathological part and use it to give a characterization of those convex capacities whose core contains at least one G-continuous measure. We then proceed to characterize the exact capacities whose core contains only G-continuous measures thus connecting some previous characterizations of impatience and myopia with core properties of exact capacities. As a dividend, a simple characterization of countably additive Borel probabilities on locally compact σ-compact metric spaces is obtained.

Suggested Citation

  • Alain Chateauneuf & Caroline Ventura, 2013. "G-continuity, impatience and myopia for Choquet multi-period utilities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00964446, HAL.
    • Handle: RePEc:hal:cesptp:hal-00964446
    DOI: 10.1016/j.jmateco.2012.10.003
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    References listed on IDEAS

    as
    1. Brown, Donald J & Lewis, Lucinda M, 1981. "Myopic Economic Agents," Econometrica, Econometric Society, vol. 49(2), pages 359-368, March.
    2. Shalev, Jonathan, 1997. "Loss aversion in a multi-period model," Mathematical Social Sciences, Elsevier, vol. 33(3), pages 203-226, June.
    3. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Prescott, Edward C & Lucas, Robert E, Jr, 1972. "A Note on Price Systems in Infinite Dimensional Space," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 416-422, June.
    6. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    7. Araujo, Aloisio, 1985. "Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience," Econometrica, Econometric Society, vol. 53(2), pages 455-461, March.
    8. 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.
    9. Chateauneuf, Alain & Rebille, Yann, 2004. "A Yosida-Hewitt decomposition for totally monotone games," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 1-9, July.
    10. Raut, L. K., 1986. "Myopic topologies on general commodity spaces," Journal of Economic Theory, Elsevier, vol. 39(2), pages 358-367, August.
    11. De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
    12. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    13. Chateauneuf, Alain & Rebille, Yann, 2004. "Some characterizations of non-additive multi-period models," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 235-250, November.
    14. Bewley, Truman F., 1981. "Stationary equilibrium," Journal of Economic Theory, Elsevier, vol. 24(2), pages 265-295, April.
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    Cited by:

    1. Faruk Gul & Paulo Natenzon & Wolfgang Pesendorfer, 2020. "Random Evolving Lotteries and Intrinsic Preference for Information," Working Papers 2020-71, Princeton University. Economics Department..
    2. Bastianello, Lorenzo & Chateauneuf, Alain, 2016. "About delay aversion," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 62-77.
    3. Bastianello, Lorenzo, 2017. "A topological approach to delay aversion," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 1-12.
    4. repec:ipg:wpaper:30 is not listed on IDEAS
    5. repec:ipg:wpaper:2013-030 is not listed on IDEAS

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