Dynamic Equilibria with Nonsmooth Utilities and Stocks: An L∞ Differential GQVI Approach

We develop a comprehensive dynamic Walrasian framework entirely in L∞ so that prices and allocations are essentially bounded, and market clearing holds pointwise almost everywhere. Utilities are allowed to be locally Lipschitz and quasi-concave; we employ Clarke subgradients to derive generalized quasi-variational inequalities (GQVIs). We endogenize inventories through a capital-accumulation constraint, leading to a differential QVI (dQVI). Existence is proved under either strong monotonicity or pseudo-monotonicity and coercivity. We establish Walras’ law, complementarity, stability and sensitivity of the equilibrium correspondence in L²-metrics, incorporate time-discounting and uncertainty on Ω×[0,T], and present convergent numerical schemes (Rockafellar–Wets penalties and extragradient). Our results close the “in mean vs pointwise” gap noted in dynamic models and connect to modern decomposition approaches for QVIs.