Final published version
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
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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 -