@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}",

note = "Funding Information: We thank two referees for detailed comments on an earlier version. Over the years we received many useful questions from students at ICE summer workshops at the University of Chicago and ZICE workshops at the University of Zurich which influenced the presentation of the material in this chapter. Felix Kubler and Karl Schmedders gratefully acknowledge financial support from the Swiss Finance Institute. Felix Kubler also acknowledges support from the ERC.",

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",

}