Mixed variational inequalities and economic equilibrium problems

Abstract

We consider rather broad classes of general economic equilibrium problems and oligopolistic equilibrium problems which can be formulated as mixed variational inequality problems. Such problems involve a continuous mapping and a convex, but not necessarily differentiable function. We present existence and uniqueness results of solutions under weakened $P$-type assumptions on the cost mapping. They enable us to establish new results for the economic equilibrium problems under consideration.