On Uniqueness of Time-Consistent Markov Policies for Quasi-Hyperbolic Consumers Under Uncertainty

We give a set of sufficient conditions for uniqueness of a time-consistent Markov stationary 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 few natural followers of optimal policy uniqueness: convergent and accurate computational algorithm, monotone comparative statics results and generalized Euler equation.

Keywords: Time consistency, Markov equilibria, Uniqueness, Stochastic games

JEL Classification: C62, C73, D91

Suggested Citation: Suggested Citation

Balbus, Lukasz and Reffett, Kevin L. and Wozny, Lukasz Patryk, On Uniqueness of Time-Consistent Markov Policies for Quasi-Hyperbolic Consumers Under Uncertainty (November 14, 2016). Available at SSRN: https://ssrn.com/abstract=2869481 or http://dx.doi.org/10.2139/ssrn.2869481