Computational aspects of the open-loop Nash equilibrium in linear quadratic games

Article Abstract:

An evaluation of the algorithm for solving the open-loop Nash equilibrium in linear quadratic differential game shows that the algorithm calculating all equilibria of the finite planning horizon case will also give equilibrium strategies if they exist. The algorithm may be used to solve linear quadratic games independent if the presence of an open-loop Nash equilibrium and that it may be generalized to the N-player case.

Statistics, Statistics (Data), Equations, Quadratic, Quadratic equations

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A nonuniform grid method for solving PDE's

Article Abstract:

A modification to the standard explicit finite differences method for solving partial differential equations in two state variables and time is presented with evaluations showing computation reduction times of 10-20 fold. The technique involves transforming the state variables to eliminate nonconstant standard deviations and instantaneous correlations to avoid oversampling the state space.

Mathematical models, Differential equations, Partial, Partial differential equations

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Industry evolution and R&D externalities

Article Abstract:

R&D externalities can reveal ranges of aggregate increasing returns to research in which an industry can bring together various equilibria. By using a theoretical model, the equilibrium dynamics are studied, proving that cyclical fluctuations on the number of firms and R&D investment may result and that long-run equilibrium is highly influenced by investors' primal beliefs.

Commercial physical research, Research & Development-Industry, Analysis, Industrial research, Influence, Industrial development, Industrialization

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