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arXiv · 2301.06729

Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy

Asrifa Sultana·Shivani Valecha
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Abstract

We study a class of quasi-variational inequality problems defined over infinite dimensional Banach space and deduce sufficient conditions for ensuring solutions to such problems under the upper semi-continuity and pseudomonotonicity assumptions on the map defining the inequalities. The special structure of the quasi-variational inequality enables us to show the occurrence of solutions for such inequalities based on the classical existence theorem for variational inequalities. This special type of quasi-variational inequalities is motivated by the pure exchange economic problems and Radner equilibrium problems for sequential trading game. Further, we study the solvability of the specific class of quasi-variational inequalities on Banach spaces in which the constraint map may admit unbounded values. Finally, we demonstrate the occurrence of dynamic competitive equilibrium for a time-dependent pure exchange economy as an application.

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Asrifa Sultana, Shivani Valecha. 2023-01-17. Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy. https://arxiv.org/abs/2301.06729

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