Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 577: Uniqueness in Infinitely Repeated Decision Problems

Nicolas Vieille and Jörgen W. Weibull ()
Additional contact information
Nicolas Vieille: Laboratoire d'Econométrie, Postal: Ecole Polytechnique and Département Economie et Finance, HEC, F-78351 Jouy en Josas, France
Jörgen W. Weibull: The Research Institute of Industrial Economics, Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden

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.

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

JEL-codes: C61; C72; C73; D90

15 pages, April 16, 2002

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