Kubler, Felix and Schmedders, Karl and Renner, Philipp (2014) Computing All Solutions to Polynomial Equations in Economics. In: Handbook of Computational Economics. Elsevier, pp. 599-652.
Full text not available from this repository.Abstract
Multiplicity of equilibria is a common problem in many economic models. In general, it is impossible to devise methods that always find all equilibria for any type of model. A notable exception are models in which all equilibria are solutions to a system of polynomial equations since there are powerful solution methods for finding all solutions to such polynomial systems. In many economic applications, equilibria can indeed be characterized as solutions to a system of polynomial equations. This handbook article provides a hands-on introduction to two solution methods for finding all solutions to polynomial systems; the first approach relies on Gröbner bases, the second approach employs all-solution homotopy methods. Several economic examples show how to compute all equilibria using modern software implementations of these two methods.