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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.

Suggested Citation

  • VIEILLE, Nicolas & WEIBULL, Jörgen W., 2002. "Uniqueness in infinitely repeated decision problems," Les Cahiers de Recherche 755, HEC Paris.
  • Handle: RePEc:ebg:heccah:0755
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    References listed on IDEAS

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    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. Geir B. Asheim, 1997. "Individual and Collective Time-Consistency," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 427-443.
    4. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    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

    Keywords

    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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