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Uniqueness in Infinitely Repeated Decision Problems

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  • Vieille, Nicolas

    (Laboratoire d'Econométrie)

  • Weibull, Jörgen W.

    ()
    (The Research Institute of Industrial Economics)

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 factor between successive periods should be non-decreasing over time, a condition met by exponential, quasi-exponential and hyperbolic discounting.

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Bibliographic Info

Paper provided by Research Institute of Industrial Economics in its series Working Paper Series with number 577.

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Length: 15 pages
Date of creation: 16 Apr 2002
Date of revision:
Handle: RePEc:hhs:iuiwop:0577

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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. 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.
  3. Goldman, Steven M, 1980. "Consistent Plans," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 533-37, April.
  4. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  5. 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.
  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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