This NSF CAREER project aims to develop foundational mathematical tools to address emerging challenges in distributed and uncertain systems, such as those in energy infrastructure, machine learning, and wireless communication. Despite recent advances in networked systems, current models and algorithms lack provable performance guarantees for a broad class of critical problems. These include (i) Generalized Nash games, where agents compete over shared resources; (ii) Bilevel optimization with constraints at both decision levels; and (iii) Saddle point problems with coupling constraints. Existing methods are not equipped to handle the complex, interdependent decision spaces or the uncertainty and decentralization that characterize these large-scale systems. This project addresses these gaps through a unified lens of Generalized Quasi-Variational Inequalities (GQVI), a powerful yet underdeveloped framework for capturing interdependent decisions under constraints. By improving solution methods for GQVI, the project will contribute to more reliable, efficient, and scalable decision-making tools for real-world applications. The educational plan includes engaging undergraduates in hands-on research experiences and training them to lead outreach activities in middle and high schools, featuring Python coding exercises and modules on optimization. Additionally, a virtual tour with faculty presentations and lab visits will simulate in-person field trips, aiming to inspire interest in ST