Dynamic Optimization and Differential Games with Applications to Economics

At IMS '97 we showed several packages for:
(1) solving simultaneous equations in real domain;
(2) obtaining necessary conditions of constrained static optimization problems;
(3) solving simultaneous nonlinear equations approximately;
(4) determining signs of expressions;
(5) solving differential equations approximately;
(6) solving boundary-value problems approximately; and
(7) solving dynamic optimization problems approximately.

We also presented applications of these packages to urban economic models [1]. However, applications are limited in the package for solving dynamic optimization problems, because there exist many problems to which the package cannot be applied. In this paper, we revise and expand it so that it can be widely used. By further expanding the package above, we can solve differential games. We first show a solution of simple differential games with Mathematica and view the optimal trajectories. We then present packages for differential games by upgrading the dynamic optimization package and show some applications to economic problems.