A research program is proposed on the application of the theory of variational enequalitites in equilibrium problems arising in transportation theory and economics. It is hoped that this approach will simplify the theory of equilibrium and will induce more effective algorithms for computing equilibria of large scale systems. Three specific projects are proposed. The first project addressed equilibria in traffic networks. A travel demand is associated with each origin-destination pair of modes of a netowrk. A travel cost is assigned to each link of the network. In the equilibrium traffic pattern, no user will be ablle to decrease his travel cost by altering his travel decisions. This can be characterized by a mathematical conidition in a form of variational inequality. The principal investigator will establish existence of equilibrium taffic patterns under weak assumptions, and will develop conceptual algorithms for finding such equilibria. The second project aims at developing a new approach for the study of general economic equilibrium, based on the theory of variational inequalitites. The main idea is to show that Walrasian equilibria can be obtained as solutions to a variational inequality, in an approporiate space.
