Uniqueness in infinitely repeated decision problems
AbstractDynamic 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.
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Bibliographic InfoPaper provided by HEC Paris in its series Les Cahiers de Recherche with number 755.
Length: 15 pages
Date of creation: 16 Apr 2002
Date of revision:
game theory; time preference; hyperbolic discounting; repeated decision problems;
Other versions of this item:
- Vieille, Nicolas & Weibull, Jörgen W., 2002. "Uniqueness in Infinitely Repeated Decision Problems," Working Paper Series 577, Research Institute of Industrial Economics.
- 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 - - Intertemporal Choice and Growth - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-12-09 (All new papers)
- NEP-CDM-2002-12-09 (Collective Decision-Making)
- NEP-GTH-2002-12-09 (Game Theory)
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