Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example

Lilia Maliar () and Serguei Maliar
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Lilia Maliar: Stanford University

Dynamic Games and Applications, 2016, vol. 6, issue 2, No 7, 243-261

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C73 D11 D80 D90 E21 H63 P16 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s13235-015-0177-8

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