Non-Concave Programming and Differential Games in Dynamic Resource Allocation Models (Nash Equilibrium, Economic Growth)
Amir, Rabah
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https://hdl.handle.net/2142/70755
Description
Title
Non-Concave Programming and Differential Games in Dynamic Resource Allocation Models (Nash Equilibrium, Economic Growth)
Author(s)
Amir, Rabah
Issue Date
1985
Department of Study
Economics
Discipline
Economics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Economics, Theory
Abstract
The thesis is comprised of two separate essays. The first, entitled "One-Sector Non-Classical Optimal Growth," considers a normative model of an aggregated economy where the objective of the central planner is the maximization of the (infinite-horizon) sum of discounted utilities subject to a convex-concave production function. The second essay, entitled "A Complete Characterization of Nash Equilibria in a Dynamic Resource Allocation Model," considers two agents, each trying to maximize the sum of his own discounted utilities subject to the common natural growth function of the resource.
In both essays, the resulting consumption paths are fully analyzed, in terms of conditions for optimality and steady-state properties. In particular, a second-order condition involving only the marginal propensities to consume is developed to account for the lack of concavity inherent in both dynamic maximization problems.
Furthermore, the first essay contains examples showing that the marginal propensity to consume may be negative (in a continuous manner), and that an unstable steady-state equilibrium may lie on the convex portion of the production function.
The second essay elaborates on the themes of selection of appropriate information structures and permissible strategy spaces to analyze such models. Finally, since stock-dependent Nash equilibria (in single-valued strategies) are generally not unique, an order property is established for the set of all such equilibria, in terms of simultaneously increasing levels of utility for the two players.
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