@article{7bc4a7036b41458c909971bc4ad29aa5,
title = "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting",
abstract = "We prove existence of time consistent equilibria in a class of dynamic models with recursive payoffs and generalized discounting involving both behavioral and normative applications. Our generalized Bellman equation method identifies and separates both: recursive and strategic aspects of the equilibrium problem and allows to determine the sufficient assumptions on preferences and stochastic transition to establish existence. In particular we show existence of minimal state space stationary Markov equilibrium (a time-consistent equilibrium) in a deterministic model of consumption-saving with beta-delta discounting and its generalized versions involving non-additive payoffs, general form certainty equivalents, as well as stochastic semi-hyperbolic and hyperbolic discounting models (over possibly unbounded state and unbounded above reward space). We also provide an equilibrium approximation method for a hyperbolic discounting model.",
keywords = "Approximation, Generalized Bellman equation, Hyperbolic discounting, Markov equilibrium, Quasi-hyperbolic discounting, Time consistency",
author = "{\L}ukasz Balbus and Kevin Reffett and {\L}ukasz Wo{\'z}ny",
note = "Funding Information: We want to thank Jean-Pierre Drugeon, Tai-Wei Hu, Martin Kaae Jensen, Jawwad Noor, Christopher Phelan, Ed Prescott, David Rahman, Michael Richter, Manuel Santos, and Jan Werner for valuable discussion during the writing of this paper. We thank participants of TUS VI Conference in Paris (2019), 6th World Congress of the Game Theory Society in Budapest (2021), RUD Conference at University of Minnesota (2021), XXIX EWET in Akko (2021) as well as participants of Econ Theory Seminar at the University of Minnesota (2020) and One World Mathematical Game Theory Seminar (GAMENET) for interesting comments on the earlier drafts of this paper. We finally want to thank two anonymous referees and the associate editor for their suggestions and all remarks. The project was financed by the National Science Center, Poland [NCN grant number UMO-2019/35/B/HS4/00346]. Reffett additionally thanks the Dean's Excellence in Research Award at the WP Carey School of Business during the Summer of 2021 for its generous support of this research. Funding Information: We want to thank Jean-Pierre Drugeon, Tai-Wei Hu, Martin Kaae Jensen, Jawwad Noor, Christopher Phelan, Ed Prescott, David Rahman, Michael Richter, Manuel Santos, and Jan Werner for valuable discussion during the writing of this paper. We thank participants of TUS VI Conference in Paris (2019), 6th World Congress of the Game Theory Society in Budapest (2021), RUD Conference at University of Minnesota (2021), XXIX EWET in Akko (2021) as well as participants of Econ Theory Seminar at the University of Minnesota (2020) and One World Mathematical Game Theory Seminar (GAMENET) for interesting comments on the earlier drafts of this paper. We finally want to thank two anonymous referees and the associate editor for their suggestions and all remarks. The project was financed by the National Science Center , Poland [NCN grant number UMO-2019/35/B/HS4/00346 ]. Reffett additionally thanks the Dean's Excellence in Research Award at the WP Carey School of Business during the Summer of 2021 for its generous support of this research. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2022",
month = sep,
doi = "10.1016/j.jet.2022.105493",
language = "English (US)",
volume = "204",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "Academic Press Inc.",
}