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

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  • Lukasz Balbus
  • Kevin Reffett
  • Lukasz Wozny

Abstract

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.

Suggested Citation

  • Lukasz Balbus & Kevin Reffett & Lukasz Wozny, 2016. "On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty," Working Papers 2016-020, Warsaw School of Economics, Collegium of Economic Analysis.
  • Handle: RePEc:sgh:kaewps:2016020
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    Cited by:

    1. Jean-Pierre Drugeon & Bertrand Wigniolle, 0. "On Markovian collective choice with heterogeneous quasi-hyperbolic discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-40.
    2. Maria Arvaniti & Chandra K. Krishnamurthy & Anne-Sophie Crépin, 2019. "Time-consistent resource management with regime shifts," CER-ETH Economics working paper series 19/329, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    3. 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.
    4. Juan Pablo Rinc'on-Zapatero, 2019. "Existence and Uniqueness of Solutions to the Stochastic Bellman Equation with Unbounded Shock," Papers 1907.07343, arXiv.org.

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    More about this item

    Keywords

    Time consistency; Markov equilibria; Uniqueness; Stochastic games; Generalized Bellman equation;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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