Working Paper No. 577

Uniqueness in Infinitely Repeated Decision Problems

Published: April 16, 2002Pages: 15Keywords: Game Theory, Time Preference; Hyperbolic Discounting; Repeated Decision ProblemsJEL-codes: C61; C72; C73; D90

Uniqueness in Infinitely Repeated Decision Problems Nicolas Vieille and Jörgen W. Weibull


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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