In this work we study the multivalued complementarity problem onthe non-negative orthant. This is carried out by describingthe asymptotic behavior of the sequence of approximatesolutions to its multivalued variational inequality formulation.By introducing new classes of multifunctions we provide severalexistence (possibly allowing unbounded solution set), stability as well assensitivity results which extend andgeneralize most of the existing ones in the literature.We also present some kind of robustness results regarding existenceof solution with respect to certain perturbations.Topological properties of the solution-set multifunction areestablished and some notions of approximable multifunctions arealso discussed. In addition,some estimates for the solution set and its asymptotic cone are derived, as well as the existence of solutions forperturbed problems is studied.
