2013
DOI: 10.1134/s1560354713060014
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A new class of problems in the calculus of variations

Abstract: IntroductionIn economic theory, and in optimal control, it has been customary to discount future gains at a constant rate δ > 0. If an individual with utility function u (c) has the choice between several streams of consumption c (t), 0 ≤ t, he or she will choose the one which maximises the present value, given by:That future gains should be discounted is well grounded in fact. On the one hand, humans prefer to enjoy goods sooner than later (and to suffer bads later than sooner), as every child-rearing parent … Show more

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Cited by 17 publications
(13 citation statements)
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“…Finally, for the derivation of the time-consistent dynamic bargaining solution, we substitute the expression of the threat point W 0 and threat strategy φ 0,nc (see Proposition 3) into (9).…”
Section: Propositionmentioning
confidence: 99%
“…Finally, for the derivation of the time-consistent dynamic bargaining solution, we substitute the expression of the threat point W 0 and threat strategy φ 0,nc (see Proposition 3) into (9).…”
Section: Propositionmentioning
confidence: 99%
“…a The paper builds on Ekeland et al (2013) and has been circulated under the title "Generations playing a Chichilnisky game". We are grateful for helpful discussions with Graciela Chichilnisky and Bård Harstad and useful comments received at SURED…”
Section: Introductionmentioning
confidence: 99%
“…However, this part of the Chichilnisky criterion may lead to more stock conservation than the time-discounted utilitarian optimum with a low-productive initial stock. Based on the notion of von Neumann-Morgenstern abstract stability, we obtain uniqueness by assuming that each generation coordinates on an almost best equilibrium and takes into account that future generations will do as well.Keywords and Phrases: Intertemporal decision making; Time inconsistency; Intergenerational equity JEL Classification Numbers: C70, D63, D91, O41, Q01a The paper builds on Ekeland et al (2013) and has been circulated under the title "Generations playing a Chichilnisky game". We are grateful for helpful discussions with Graciela Chichilnisky and Bård Harstad and useful comments received at SURED…”
mentioning
confidence: 99%
“…An "equilibrium" control is therefore one such that any deviation from it at any time instant will be worse off. The study on time inconsistency by economists can be dated back to Stroz [23] and Phelps ([21, 22]) in models with discrete time (see [17] and [18] for further developments), and adapted by Karp ([15,16]), and by Ekeland and Lazrak ([5,6,7,8,9,10]) to the case of continuous time. In the LQ control problems, Yong [24] studied a time-inconsistent deterministic model and derived equilibrium controls via some integral equations.…”
Section: Introductionmentioning
confidence: 99%