Inverse Variational Inequality Approach and Applications

Abstract

It is well known that a dynamic oligopolistic market equilibrium problem can be studied as an evolutionary variational inequality and this problem is approached as a problem of profit optimization for the firms. On the contrary, in this article, with the help of an inverse variational formulation, the behavior of control policies for an oligopolistic market equilibrium problem, whose aim is to regulate the exportation through the adjustment of taxes on the firms, is studied. This is considered as a policymaker optimization problem. More precisely, a definition of equilibrium for the firms by using the Lagrange multipliers is provided together to the optimal regulatory tax definition. Moreover an existence result is given and, at last, a numerical example is analyzed.

Keywords:

• Dynamic oligopolistic market equilibrium problem
• Evolutionary variational inequality
• Inverse variational inequality
• Lagrange multipliers
• Policy-maker optimization problem
• Production and demand excesses

Mathematics Subject Classification:

• 49J40
• 58E35
• 91A10
• 49N45

ACKNOWLEDGMENTS

The authors thank the referee for helpful comments and suggestions that led to a clearer presentation of this work.

Part of the special issue, “Variational Analysis and Applications.”