Maliar, Lilia, Maliar, Serguei
Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example
Dynamic Games and Applications. 2016, 6(2): 243-261. doi:10.1007/s13235-015-0177-8
URI: http://hdl.handle.net/10045/62608
DOI: 10.1007/s13235-015-0177-8
ISSN: 2153-0785 (Print)
Abstract: 
The literature that conducts numerical analysis of equilibrium in models with hyperbolic (quasi-geometric) discounting reports difficulties in achieving convergence. Surprisingly, numerical methods fail to converge even in a simple, deterministic optimal growth problem that has a well-behaved, smooth closed-form solution. We argue that the reason for nonconvergence is that the generalized Euler equation has a continuum of smooth solutions, each of which is characterized by a different integration constant. We propose two types of restrictions that can rule out the multiplicity: boundary conditions and shape restrictions on equilibrium policy functions. With these additional restrictions, the studied numerical methods deliver a unique smooth solution for both the deterministic and stochastic problems in a wide range of the model’s parameters.
Keywords:Hyperbolic discounting, Quasi-geometric discounting, Time inconsistency, Markov perfect equilibrium, Markov games, Turnpike theorem, Neoclassical growth model, Endogenous gridpoints, Envelope condition
Springer Science+Business Media New York
info:eu-repo/semantics/article