A network equilibrium formulation of market disequilibrium and variational inequalities

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Abstract
In this article, we consider an asymmetric market disequilibrium model in a spatial setting in the case of rigid prices and/or controls. In this problem, the markets need no longer clear. We show that the disequilibrium problem can be reformulated as an equilibrium problem over an abstract network with special structure. We then propose a network decomposition algorithm for the computation of the solution that exploits the structure and establishes convergence results using the theory of variational inequalities. Our computational results demonstrate the suitability of this approach for large‐scale market problems.