Uniqueness in infinitely repeated decision problems

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Uniqueness in infinitely repeated decision problems

Author Info

VIEILLE, Nicolas
WEIBULL, Jörgen W.

Additional information is available for the following registered author(s):

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.

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Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 755.

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Length: 15 pages
Date of creation: 16 Apr 2002
Date of revision:
Handle: RePEc:ebg:heccah:0755

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Paper
- Vieille, Nicolas & Weibull, Jörgen W., 2002. "Uniqueness in Infinitely Repeated Decision Problems," Working Paper Series 577, Research Institute of Industrial Economics. [Downloadable!]

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Kocherlakota, Narayana R., 1996. "Reconsideration-Proofness: A Refinement for Infinite Horizon Time Inconsistency," Games and Economic Behavior, Elsevier, vol. 15(1), pages 33-54, July. [Downloadable!] (restricted)
Goldman, Steven M, 1980. "Consistent Plans," Review of Economic Studies, Blackwell Publishing, vol. 47(3), pages 533-37, April. [Downloadable!] (restricted)
Peleg, Bezalel & Yaari, Menahem E, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Blackwell Publishing, vol. 40(3), pages 391-401, July. [Downloadable!] (restricted)
Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
Other versions:
- Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
Sáez-Martí, María & Weibull, Jörgen W., 2002. "Discounting and Future Selves," Working Paper Series 575, Research Institute of Industrial Economics. [Downloadable!]
Asheim, G.B., 1991. "Individual and Collective Time Consistency," Papers 9169, Tilburg - Center for Economic Research.
Other versions:
- Geir B. Asheim, 1995. "Individual and Collective Time-Consistency," Discussion Papers 1128, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
- Asheim, G.B., 1996. "Individual and Collective Time-Consistency," Memorandum 20/1996, Oslo University, Department of Economics.
- Asheim, Geir B, 1997. "Individual and Collective Time-Consistency," Review of Economic Studies, Blackwell Publishing, vol. 64(3), pages 427-43, July. [Downloadable!] (restricted)

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