A new resolution method for the parametric linear complementarity problem

An original method is presented to solve the parametric linear complementarity problem. To solve such a problem requires to identify the values taken by the solution of a linear complementarity problem where some of its right-hand side terms vary in prescribed domain. This class of problems allows, among others, to deal with linear market equilibrium problems with varying prices: it allows to identify how the equilibrium point varies when the prices vary over a set of given values. This method is illustrated through an application related to the institution of ecological taxes on the Western European natural gas market.