Spectral analysis of coupled linear complementarity problems

This note deals with the so-called cone-constrained bivariate eigenvalue problem. The equilibrium model under consideration is a system of linear complementarity problemsP∋x⊥(Ax+By-λx)∈P∗,Q∋y⊥(Cx+Dy-μy)∈Q∗involving two closed convex cones and their corresponding duals. We study the set of pairs (λ,μ)∈R2(λ,μ)∈R2 for which this system has a “nontrivial” solution (x,y)∈Rn+m(x,y)∈Rn+m. We discuss also the link between the cone-constrained version and the unconstrained one.