The parametric linear complementarity problem is given by the conditions:q + αp + Mz ⩾ 0,α ⩾ 0,z ⩾ 0,z T (q + αp + Mz) = 0. Under the assumption thatM is a P-matrix, Cottle proved that the solution mapz(α) of the above problem is montonically nondecreasing in the parameterα for every nonnegativeq and everyp if and only ifM is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.