International Journal of Game Theory

, Volume 44, Issue 1, pp 83–112 | Cite as

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

Article

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.

Keywords

Time consistency Markov equilibria Stochastic games  Constructive methods 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics, Computer Sciences and EconometricsUniversity of Zielona GóraZielona GoraPoland
  2. 2.Department of EconomicsArizona State UniversityTempeUSA
  3. 3.Department of Quantitative EconomicsWarsaw School of EconomicsWarsawPoland

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