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

Francesco Rania ()
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Francesco Rania: Department of Law, Economics and Sociology, Magna Græcia University of Catanzaro, Viale Europa, Loc. Germaneto, 88100 Catancaro, Italy

Mathematics, 2025, vol. 13, issue 21, 1-45

Abstract: 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, and the complementarity, stability, and sensitivity of the equilibrium correspondence in L 2 -metrics, incorporate time-discounting and uncertainty into 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.

Keywords: Walrasian dynamic competitive equilibrium; (generalized) quasi-variational inequalities; weak-∗ compactness; Clarke subgradients; differential QVI; stability; numerical schemes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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