Les Cahiers de Recherche - HEC Paris
No 755:
Uniqueness in infinitely repeated decision problems
Nicolas VIEILLE and Jörgen W. WEIBULL
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.
Keywords: game theory; time preference; hyperbolic discounting; repeated decision problems; (follow links to similar papers)
JEL-Codes: C61; C72; C73; D90; (follow links to similar papers)
15 pages, April 16, 2002
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