Variational Inequality Formulation and Algorithmic Computation of Dynamic Economic Equilibria

This paper presents a computational implementation of a dynamic Walrasian equilibrium model in continuous time, formulated via variational inequality (VI) and quasi-variational inequality (QVI) frameworks. Building on the theoretical existence and stability results of the underlying equilibrium model, we discretize the time interval and implement a projected extragradient algorithm on the price simplex to compute equilibrium prices and allocations. We illustrate convergence behavior in a stylized Cobb-Douglas example and discuss the effects of discretization mesh size, stepsize selection, and algorithm performance. Numerical experiments demonstrate the practicality of the method, bridging the gap between theory and implementation. We also comment on mesh-independence, per-iteration complexity, and the role of strong monotonicity in achieving linear convergence. The computational study extends the purely theoretical framework by showing how real-world discretization and algorithmic choices impact convergence.