Dynamic equilibrium model for spatial auction markets

Abstract

Spatial equilibrium models are utilized for description of behavior and for management of complex systems containing many interacting elements, with taking into account their spatial distribution. We consider such a system of auction markets joined by transmission lines subject to joint balance and capacity flows constraints for a certain time period propose a primal-dual system of variational inequalities whose solutions yield an equilibrium trajectory of this system. A splitting type method is proposed to find a solution.