Computing All Solutions to Polynomial Equations in Economics

Felix Kubler*, Philipp Renner, Karl H Schmedders

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationHandbook of Computational Economics
PublisherElsevier B.V.
Pages599-652
Number of pages54
DOIs
StatePublished - 2014

Publication series

NameHandbook of Computational Economics
Volume3
ISSN (Print)1574-0021

Keywords

  • All-solution homotopies
  • Gröbner bases
  • Multiple equilibria
  • Polynomial equations

ASJC Scopus subject areas

  • Economics and Econometrics
  • Computer Science Applications

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