@article{a421943647dc45c3a27ca8e8c4ac10bf,
title = "On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty",
abstract = "We give a set of sufficient conditions for uniqueness of a time-consistent stationary Markov consumption policy for a quasi-hyperbolic household under uncertainty. To the best of our knowledge, this uniqueness result is the first presented in the literature for general settings, i.e. under standard assumptions on preferences, as well as some new condition on a transition probability. This paper advocates a “generalized Bellman equation” method to overcome some predicaments of the known methods and also extends our recent existence result. Our method also works for returns unbounded from above. We provide a few natural extensions of optimal policy uniqueness: convergent and accurate computational algorithm, monotone comparative statics result and generalized Euler equation.",
keywords = "Generalized Bellman equation, Markov equilibrium, Time consistency, Uniqueness",
author = "{\L}ukasz Balbus and Kevin Reffett and {\L}ukasz Wo{\'z}ny",
note = "Funding Information: We thank Robert Becker, Madhav Chandrasekher, Manjira Datta, Pawe{\l} Dziewulski, Amanda Friedenberg, Ed Green, Seppo Heikkil{\"a}, Len Mirman, Peter Streufert, and especially Ed Prescott, as well participants of our SAET 2013 session and DIET 2013 conference for helpful conversations on the topics of this paper. Balbus and Wo{\'z}ny thank the NCN grant No. UMO-2016/23/B/HS4/02398 . Reffett would like to thank the Dean's Excellence in Research Summer Grant Program at ASU for their generous support of his research. All the usual caveats apply. Funding Information: We thank Robert Becker, Madhav Chandrasekher, Manjira Datta, Pawe{\l} Dziewulski, Amanda Friedenberg, Ed Green, Seppo Heikkil{\"a}, Len Mirman, Peter Streufert, and especially Ed Prescott, as well participants of our SAET 2013 session and DIET 2013 conference for helpful conversations on the topics of this paper. Balbus and Wo{\'z}ny thank the NCN grant No. UMO-2016/23/B/HS4/02398. Reffett would like to thank the Dean's Excellence in Research Summer Grant Program at ASU for their generous support of his research. All the usual caveats apply. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2018",
month = jul,
doi = "10.1016/j.jet.2018.04.003",
language = "English (US)",
volume = "176",
pages = "293--310",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "Academic Press Inc.",
}