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Uniqueness in Infinitely Repeated Decision Problems


  • Vieille, Nicolas

    (Laboratoire d'Econométrie)

  • Weibull, Jörgen W.

    () (The Research Institute of Industrial Economics)


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.

Suggested Citation

  • Vieille, Nicolas & Weibull, Jörgen W., 2002. "Uniqueness in Infinitely Repeated Decision Problems," Working Paper Series 577, Research Institute of Industrial Economics.
  • Handle: RePEc:hhs:iuiwop:0577

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    References listed on IDEAS

    1. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
    2. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
    3. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    4. Geir B. Asheim, 1997. "Individual and Collective Time-Consistency," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 427-443.
    5. Steven M. Goldman, 1980. "Consistent Plans," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 533-537.
    6. 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.
    7. Sáez-Martí, María & Weibull, Jörgen W., 2002. "Discounting and Future Selves," Working Paper Series 575, Research Institute of Industrial Economics.
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    More about this item


    Game Theory; Time Preference; Hyperbolic Discounting; Repeated Decision Problems;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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