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Uniqueness in infinitely repeated decision problems

  • VIEILLE, Nicolas
  • WEIBULL, Jörgen W.

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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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
Contact details of provider: Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
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  1. Asheim, G.B., 1996. "Individual and Collective Time-Consistency," Memorandum 20/1996, Oslo University, Department of Economics.
  2. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
  3. 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.
  4. 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.
  5. Goldman, Steven M, 1980. "Consistent Plans," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 533-37, April.
  6. Sáez-Martí, María & Weibull, Jörgen W., 2002. "Discounting and Future Selves," Working Paper Series 575, Research Institute of Industrial Economics.
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