An inverse variational inequality approach to the evolutionary spatial price equilibrium problem

It is well-known that the time-dependent spatial price equilibrium problem can be transformed into and studied as an evolutionary variational inequality. However, in some situations, control policies may be imposed to the end of regulating the amounts of production and consumption. As a consequence, the problem becomes a time-dependent spatial price equilibrium control problem and is formulated as an evolutionary inverse variational inequality. The existence of solutions is then investigated and a numerical example is also provided.