Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses

The paper is devoted to generalize a previous model of the dynamic oligopolistic market equilibrium problem allowing the presence of production excesses and assuming, in a more reasonable way that the total amounts of commodity shipments from a firm to all the demand markets be upper bounded. First, we give equilibrium conditions in terms of the well‐known dynamic Cournot–Nash equilibrium principle. Then we show that such conditions can be expressed in terms of Lagrange multipliers; namely, by means of an utility function, prove that both equilibrium conditions can be equivalently expressed by a variational inequality. The variational formulation allows us to provide existence theorems and qualitative properties for equilibrium solutions. At last, a numerical example illustrates the results obtained.