An Inverse Problem for the Dynamic Oligopolistic Market Equilibrium Problem in Presence of Excesses

The theory of evolutionary variational inequalities fits very well in a lot of optimization problems, like for example the dynamic oligopolistic market equilibrium problem that we describe in this paper. But here, the authors analyze the behavior of control policies whose aim is to regulate the exportation through the adjustments of supply taxes or incentives on the firms. This is considered as a policy-maker optimization problem. This aspect is studied with the help of an inverse evolutionary variational formulation. Moreover, a characterization of the inverse variational inequality with an appropriate evolutionary variational inequality is given. Unlike the paper (Barbagallo & Mauro, 2013), here the authors explore the possibility of presence of production and demand excesses. Moreover, we provide a definition of equilibrium for the firms by using the infinite dimensional duality theory and later we define an optimal regulatory tax. Finally, we present a numerical scheme in order to compute the equilibrium solution of the inverse variational inequality that models the policy-maker's point of view for the dynamic oligopolistic market equilibrium problem in presence of excesses, then we provide a numerical example.