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Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers

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  • Łukasz Balbus
  • Kevin Reffett
  • Łukasz Woźny

    ()

Abstract

We study the question of existence and computation of time-consistent Markov policies of quasi-hyperbolic consumers under a stochastic transition technology in a general class of economies with multidimensional action spaces and uncountable state spaces. Under standard complementarity assumptions on preferences, as well as a mild geometric condition on transition probabilities, we prove existence of time-consistent solutions in Markovian policies, and provide conditions for the existence of continuous and monotone equilibria. We present applications of our methods to habit formation models, environmental policies, and models of consumption under borrowing constraints, and hence show how our methods extend the results obtained by Harris and Laibson (Econometrica 69:935–957, 2001 ) to a broad class of dynamic economies. We also present a simple successive approximation scheme for computing extremal equilibrium, and provide some results on the existence of monotone equilibrium comparative statics in the model’s deep parameters. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2015. "Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 83-112, February.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:1:p:83-112
    DOI: 10.1007/s00182-014-0420-3
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    Cited by:

    1. Robert A. Becker & Juan Pablo Rincón-Zapatero, 2017. "Arbitration and Renegotiation in Trade Agreements," Caepr Working Papers 2017-007 Classification-D, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    2. Lukasz Wozny, 2016. "Repeated moral hazard with costly self-control," Working Papers 2016-017, Warsaw School of Economics, Collegium of Economic Analysis.
    3. Robert Becker & Juan Pablo Rincon-Zapatero, 2018. "Recursive Utility and Thompson Aggregators, II: Uniqueness of the Recursive Utility Representation," Caepr Working Papers 2018-008 Classification-D, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    4. 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.
    5. Łukasz Balbus & Łukasz Woźny, 2016. "A Strategic Dynamic Programming Method for Studying Short-Memory Equilibria of Stochastic Games with Uncountable Number of States," Dynamic Games and Applications, Springer, vol. 6(2), pages 187-208, June.
    6. 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.
    7. Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2016. "Non-paternalistic intergenerational altruism revisited," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 27-33.
    8. Robert Becker & Juan Pablo Rincon-Zapatero, 2018. "Recursive Utility and Thompson Aggregators, I: Constructive Existence Theory for the Koopmans Equation," Caepr Working Papers 2018-006 Classification-D, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.

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