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Computing All Solutions to Polynomial Equations in Economics

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Computing All Solutions to Polynomial Equations in Economics. / Kubler, Felix; Schmedders, Karl; Renner, Philipp.
Handbook of Computational Economics. Vol. 3 Elsevier, 2014. p. 599-652.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

Harvard

Kubler, F, Schmedders, K & Renner, P 2014, Computing All Solutions to Polynomial Equations in Economics. in Handbook of Computational Economics. vol. 3, Elsevier, pp. 599-652. https://doi.org/10.1016/B978-0-444-52980-0.00011-6

APA

Kubler, F., Schmedders, K., & Renner, P. (2014). Computing All Solutions to Polynomial Equations in Economics. In Handbook of Computational Economics (Vol. 3, pp. 599-652). Elsevier. https://doi.org/10.1016/B978-0-444-52980-0.00011-6

Vancouver

Kubler F, Schmedders K, Renner P. Computing All Solutions to Polynomial Equations in Economics. In Handbook of Computational Economics. Vol. 3. Elsevier. 2014. p. 599-652 doi: 10.1016/B978-0-444-52980-0.00011-6

Author

Kubler, Felix ; Schmedders, Karl ; Renner, Philipp. / Computing All Solutions to Polynomial Equations in Economics. Handbook of Computational Economics. Vol. 3 Elsevier, 2014. pp. 599-652

Bibtex

@inbook{d119445ffe4c457185cc50d390f17c5b,
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 = "Multiple equilibria, Polynomial equations, Gr{\"o}bner bases, All-solution homotopies",
author = "Felix Kubler and Karl Schmedders and Philipp Renner",
year = "2014",
doi = "10.1016/B978-0-444-52980-0.00011-6",
language = "English",
volume = "3",
pages = "599--652",
booktitle = "Handbook of Computational Economics",
publisher = "Elsevier",

}

RIS

TY - CHAP

T1 - Computing All Solutions to Polynomial Equations in Economics

AU - Kubler, Felix

AU - Schmedders, Karl

AU - Renner, Philipp

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Multiple equilibria

KW - Polynomial equations

KW - Gröbner bases

KW - All-solution homotopies

U2 - 10.1016/B978-0-444-52980-0.00011-6

DO - 10.1016/B978-0-444-52980-0.00011-6

M3 - Chapter

VL - 3

SP - 599

EP - 652

BT - Handbook of Computational Economics

PB - Elsevier

ER -