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      Strategic interaction and dynamics under endogenous time preference

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      Author(s)
      Camacho, C.
      Saglam, C.
      Turan, A.
      Date
      2013
      Source 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
      Article
      Item 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.
      Keywords
      Supermodular games
      Strategic growth
      Lattice programming
      Endogenous time preference
      Permalink
      http://hdl.handle.net/11693/11554
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jmateco.2013.05.002
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