Tackling Multiplicity of Equilibria with Gröbner Bases

Multiplicity of equilibria is a prevalent problem in many economic models. Oftenequilibria are characterized as solutions to a system of polynomial equations. This pa-per gives an introduction to the application of GrÄobner basis methods for ¯nding allsolutions of a polynomial system. The Shape Lemma, a key result from algebraic ge-ometry, states under mild assumptions that a given equilibrium system has the samesolution set as a much simpler triangular system. Essentially the computation of allsolutions then reduces to ¯nding all roots of a single polynomial in a single unknown.[...]