Abstract
We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx t+1=h(x t ), defined on the state space, we find two discount factors 0 < δ* ≤** < 1 having the following properties. For any fixed discount factor 0 < δ < δ*, the dynamic system is the solution to some concave problem. For any discount factor δ** < δ < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound δ** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.
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Communicated by W. Stadler
This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.
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Montrucchio, L. Dynamic complexity of optimal paths and discount factors for strongly concave problems. J Optim Theory Appl 80, 385–406 (1994). https://doi.org/10.1007/BF02207771
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DOI: https://doi.org/10.1007/BF02207771