Mendonça, G. P. A. de (2013) Nonlinear and evolutionary phenomena in deterministic growing economies. PhD thesis, University of Warwick.

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Abstract

We discuss the implications of nonlinearity in competitive models of optimal
endogenous growth. Departing from a simple representative agent setup with
convex risk premium and investment adjustment costs, we define an open economy
dynamic optimization problem and show that the optimal control solution is given
by an autonomous nonlinear vector field in <3 with multiple equilibria and no optimal
stable solutions. We give a thorough analytical and numerical analysis of this
system qualitative dynamics and show the existence of local singularities, such as
fold (saddle-node), Hopf and Fold-Hopf bifurcations of equilibria. Finally, we discuss
the policy implications of global nonlinear phenomena. We focus on dynamic
scenarios arising in the vicinity of Fold-Hopf bifurcations and demonstrate the existence
of global dynamic phenomena arising from the complex organization of the
invariant manifolds of this system. We then consider this setup in a non-cooperative
differential game environment, where asymmetric players choose open loop no feedback
strategies and dynamics are coupled by an aggregate risk premium mechanism.
When only convex risk premium is considered, we show that these games have a
specific state-separability property, where players have optimal, but naive, beliefs
about the evolution of the state of the game. We argue that the existence of optimal
beliefs in this fashion, provides a unique framework to study the implications
of the self-confirming equilibrium (SCE) hypothesis in a dynamic game setup. We
propose to answer the following question. Are players able to concur on a SCE,
where their expectations are self-fulfilling? To evaluate this hypothesis we consider
a simple conjecture. If beliefs bound the state-space of the game asymptotically
and strategies are Lipschitz continuous, then it is possible to describe SCE solutions
and evaluate the qualitative properties of equilibrium. If strategies are not smooth,
which is likely in environments where belief-based solutions require players to learn
a SCE, then asymptotic dynamics can be evaluated numerically as a Hidden Markov
Model (HMM). We discuss this topic for a class of games where players lack the
relevant information to pursue their optimal strategies and have to base their decisions
on subjective beliefs. We set up one of the games proposed as a multi-objective
optimization problem under uncertainty and evaluate its asymptotic solution as a
multi-criteria HMM.We show that under a simple linear learning regime there is convergence
to a SCE and portray strong emergence phenomena as a result of persistent
uncertainty.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Nonlinear theories, Endogenous growth (Economics) -- Mathematical models , Evolutionary economics
Official Date:	October 2013
Institution:	University of Warwick
Theses Department:	Mathematics Institute; Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	MacKay, R. S. (Robert Sinclair); Deissenberg, Christophe
Sponsors:	Portugal; Fundação para a Ciência e a Tecnologia (FCT); Engineering and Physical Sciences Research Council (EPSRC)
Extent:	viii, 164 leaves : illustrations.
Language:	eng

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