Being serious about non-commitment: subgame perfect equilibrium in continuous time

By Ivar Ekeland, Ali Lazrak. 2006

183 citations recorded by the source corpus.

This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is reminescent of the classical Hamilton-Jacobi-Bellman equation of optimal control, but with a non-local term. We give a local existence result, and several examples in the consumption saving problem. The analysis is then applied to suggest that non constant discount rates generate an indeterminacy of the steady state in the Ramsey growth model. Despite its indeterminacy, the steady state level is robust to small deviations from constant discount rates.

Subfields: Economics and Econometrics, General Decision Sciences, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7852eab8873766f1f70b77bd3cccbde61d83bc73

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Citations in the corpus

Investment and consumption without commitment (2007, methodology): “Pseudo-exponential discount rates were rst considered in the context of timeinconsistency in [ 4 ].”
The golden rule when preferences are time inconsistent (2010, methodology): “Previous versions of this paper have been made available in [4,5].”
Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion (2013, background): “For optimal consumption and investment problems with non-exponential discounting have recently been studied from the game theoretic point of view by Ekeland and Lazrak (2006), Ekeland and Pirvu (2007) and Ekeland et al. (2012).”
A General Theory of Markovian Time Inconsistent Stochastic Control Problems (2010, background): “In the interesting, and mathematically very advanced, papers [3] and [4], the authors consider optimal consumption and investment under hyperbolic discounting (Problem 1 in our list above) in deterministic and stochastic models from the above game theoretic point of view.”
Optimal stopping under probability distortion. (2011, unknown): “Now define the following distribution set D and quantile set Q: D := { F : R 7→ [0, 1] ∣∣∣ F is the CDF of Sτ , for some τ ∈ T } , (9) Q := { G : [0, 1) 7→ R ∣∣∣ G = F−1 for some F ∈ D} .”