Strategic interaction and dynamics under endogenous time preference
Date
2013Source Title
Journal of Mathematical Economics
Print ISSN
0304-4068
Electronic ISSN
1873-1538
Publisher
Elsevier
Volume
49
Issue
4
Pages
291 - 301
Language
English
Type
ArticleItem Usage Stats
137
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Abstract
This paper presents a strategic growth model with endogenous time preference. Due to the potential
lack of concavity and the differentiability of the value functions associated with each agent’s problem,
we employ the theory of monotone comparative statics and supermodular games based on order and
monotonicity properties on lattices. In particular, we provide the sufficient conditions of supermodularity
for dynamic games with open-loop strategies based on two fundamental elements: the ability to order
elements in the strategy space of the agents and the strategic complementarity which implies upward
sloping best responses. The supermodular game structure of the model lets us provide the existence and
the monotonicity results on the greatest and the least equilibria. We sharpen these results by showing
the differentiability of the value function and the uniqueness of the best response correspondences
almost everywhere and show that the stationary state Nash equilibria tend to be symmetric. Finally, we
numerically analyze to what extent the strategic complementarity inherent in agents’ strategies can alter
the convergence results that could have emerged under a single agent optimal growth model. In particular,
we show that the initially rich can pull the poor out of the poverty trap even when sustaining a higher
level of steady state capital stock for itself.