@inbook{70f63276945247e4a985f3158a3a778a,

title = "Computing All Solutions to Polynomial Equations in Economics",

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 Gr{\"o}bner 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.",

keywords = "All-solution homotopies, Gr{\"o}bner bases, Multiple equilibria, Polynomial equations",

author = "Felix Kubler and Philipp Renner and Schmedders, {Karl H}",

year = "2014",

doi = "10.1016/B978-0-444-52980-0.00011-6",

language = "English (US)",

series = "Handbook of Computational Economics",

publisher = "Elsevier B.V.",

pages = "599--652",

booktitle = "Handbook of Computational Economics",

}