Variational inequalities on a class of structured tensors

In this paper we study variational inequalities defined on a class of structured tensors, and provide existence and uniqueness results. An important special case considered is the nonlinear complementarity problem, recently introduced in the tensor-based form. Both the tensor variational inequality problem and the tensor complementarity problem have application in finding the Nash equilibrium point of the n person noncooperative game. Moreover, we introduce the generalized tensor variational inequalities in the tensor Hilbert space endowed with a inner product between two tensors. At last, we apply this new tool to analyze an extension of the oligopolistic market equilibrium problem.