On nonsmooth hierarchical generalized Nash equilibrium problems via hierarchical generalized variational inequalities

We study hierarchical Generalized Nash Equilibrium Problems whose shared feasible region is implicitly defined as the solution set of a lower-level Nash game. We allow the presence of nonsmooth terms in the objectives of both the players of the GNEP and the NEP. To compute variational equilibria, we design first-order projected Tikhonov-type methods and establish their convergence and complexity guarantees. The practical impact is demonstrated through numerical experiments on a multi-portfolio selection model with real-world financial datasets. Moreover, we develop a unifying inexactness framework for variational and game-theoretic models (Variational Inequalities, Minty variational inequalities, Natural-Map problems, and Nash Equilibrium Problems). For each problem class we formalize an inexact counterpart and derive tight implication chains and stability bounds that quantify how approximation errors propagate across formulations. These results clarify how algorithmic stopping tolerances or modeling inaccuracies in one formulation translate into inexactness levels in the others, using only problem-dependent constants and the original inexactness level.