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Uniqueness in infinitely repeated decision problems

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  • VIEILLE, Nicolas
  • WEIBULL, Jörgen W.

Abstract

Dynamic decision-making without commitment is usually modelled as a game between the current and future selves of the decision maker. It has been observed that if the time-horizon is infinite, then such games may have multiple subgame-perfect equilibrium solutions. We provide a sufficient condition for uniqueness in a class of such games, namely infinitely repeated decision problems with discounting. The condition is two-fold: the range of possible utility levels in the decision problem should be bounded from below, and the discount function should exhibit weakly increasing patience, that is, the ratio between the discount factors attached to periods t + 1 and t should be non-decreasing in t, a condition met by exponential, quasi-exponential and hyperbolic discounting.

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Bibliographic Info

Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 755.

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Length: 15 pages
Date of creation: 16 Apr 2002
Date of revision:
Handle: RePEc:ebg:heccah:0755

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Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
Web page: http://www.hec.fr/
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Keywords: game theory; time preference; hyperbolic discounting; repeated decision problems;

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  1. Geir B. Asheim, 1995. "Individual and Collective Time-Consistency," Discussion Papers 1128, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Kocherlakota, Narayana R., 1996. "Reconsideration-Proofness: A Refinement for Infinite Horizon Time Inconsistency," Games and Economic Behavior, Elsevier, vol. 15(1), pages 33-54, July.
  3. Sáez-Martí, María & Weibull, Jörgen W., 2002. "Discounting and Future Selves," Working Paper Series 575, Research Institute of Industrial Economics.
  4. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
  5. Peleg, Bezalel & Yaari, Menahem E, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 391-401, July.
  6. Goldman, Steven M, 1980. "Consistent Plans," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 533-37, April.
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