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On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty

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  • Balbus, Łukasz
  • Reffett, Kevin
  • Woźny, Łukasz

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.

Suggested Citation

  • Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2018. "On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty," Journal of Economic Theory, Elsevier, vol. 176(C), pages 293-310.
  • Handle: RePEc:eee:jetheo:v:176:y:2018:i:c:p:293-310
    DOI: 10.1016/j.jet.2018.04.003
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    Cited by:

    1. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    2. Juan Pablo Rinc'on-Zapatero, 2019. "Existence and Uniqueness of Solutions to the Stochastic Bellman Equation with Unbounded Shock," Papers 1907.07343, arXiv.org.

    More about this item

    Keywords

    Time consistency; Markov equilibrium; Uniqueness; Generalized Bellman equation;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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