Abstract:
This paper investigates an infinite-horizon problem in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern for the well-being of future generations. We show that there are no optimal solutions, but that there are equilibrium strateges, i.e. Nash equilibria of the leader-follower game between successive generations. To solve the problem, we approximate the Chichilnisky criterion by a biexponential criterion, we characterize its equilibria by a pair of coupled differential equations of HJB type, and we go to the limit. We find all the equilibrium strategies for the Chichilnisky criterion. The mathematical analysis is difficult because one has to solve an implicit differential equation in the sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak.
Research Fund for the Doctoral Program of Higher Education
Ivar Ekeland acknowledges the financial support of the Chaire de Développement Durable at the Université de Paris-Dauphine. Yiming Long’s research was partially supported by NNSF, MCME, RFDP, LPMC of MOE of China, and Nankai University. Qinglong Zhou’s research was partially supported by the Chern Institute of Mathematics, Nankai University, CEREMADE of Université Paris Dauphine, and the IHES.
\Bibitem{EkeLonZho13}
\by Ivar Ekeland, Yiming Long, Qinglong Zhou
\paper A New Class of Problems in the Calculus of Variations
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 553--584
\mathnet{http://mi.mathnet.ru/rcd149}
\crossref{https://doi.org/10.1134/S1560354713060014}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3146579}
\zmath{https://zbmath.org/?q=an:1286.49025}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000329108900001}
Linking options:
https://www.mathnet.ru/eng/rcd149
https://www.mathnet.ru/eng/rcd/v18/i6/p553
This publication is cited in the following 16 articles:
Valeriia Chukaeva, Julia de Frutos Cachorro, Jesús Marín-Solano, “Groundwater Extraction for Irrigation Purposes: The Case of Asymmetric Players”, Water Econs. Policy, 10:02 (2024)
P. Koundouri, G. I. Papayiannis, A. N. Yannacopoulos, Implementing the UN Sustainable Development Goals – Regional Perspectives, SDGs in the European Region, 2023, 29
Qinglong Zhou, Gaofeng Zong, “A stochastic linear-quadratic differential game with time-inconsistency”, era, 30:7 (2022), 2550
P. Koundouri, G. I. Papayiannis, A. N. Yannacopoulos, Implementing the UN Sustainable Development Goals – Regional Perspectives, SDGs in the European Region, 2022, 1
Bartaloni F., “Existence of the Optimum in Shallow Lake Type Models With Hysteresis Effect”, J. Optim. Theory Appl., 190:2 (2021), 358–392
Castaner A., Marin-Solano J., Ribas C., “A Time Consistent Dynamic Bargaining Procedure in Differential Games With Hterogeneous Discounting”, Math. Method Oper. Res., 93:3 (2021), 555–584
Cachorro Julia de Frutos, Marin-Solano J., Navas J., “Competition Between Different Groundwater Uses Under Water Scarcity”, Water Resour. Econ., 33 (2021), 100173
Jesús Marín-Solano, “Dynamic Bargaining and Time-Consistency in Linear-State and Homogeneous Linear-Quadratic Cooperative Differential Games”, Int. Game Theory Rev., 23:04 (2021)
Bartaloni F., “Existence of Solutions to Shallow Lake Type Optimal Control Problems”, J. Optim. Theory Appl., 185:2 (2020), 384–415
Wei Yan, Jiongmin Yong, The IMA Volumes in Mathematics and its Applications, 164, Modeling, Stochastic Control, Optimization, and Applications, 2019, 533
M. Kitti, “Sustainable social choice under risk”, Math. Soc. Sci., 94 (2018), 19–31
G. B. Asheim, I. Ekeland, “Resource conservation across generations in a Ramsey–Chichilnisky model”, Econ. Theory, 61:4 (2016), 611–639
J. Marin-Solano, “Group inefficiency in a common property resource game with asymmetric players”, Econ. Lett., 136 (2015), 214–217
Graciela Chichilnisky, Wiley Encyclopedia of Management, 2015, 1
Citation in format AMSBIB
Contact us: