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.

Interdisciplinary European Studies

The European Union in a Changing World Order

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This book explores how the European Union responds to the ongoing challenges to the liberal international order. These challenges arise both within the EU itself and beyond its borders, and put into question the values of free trade and liberal democracy. 

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