Addressing Hierarchical Jointly-Convex Generalized Nash Equilibrium Problems with Nonsmooth Payoffs

We consider a Generalized Nash Equilibrium Problem whose joint feasible region is implicitly defined as the solution set of another Nash game. This structure arises e.g. in multi-portfolio selection contexts, whenever agents interact at different hierarchical levels. We consider nonsmooth terms in all players' objectives, to promote, for example, sparsity in the solution. Under standard assumptions, we show that the equilibrium problems we deal with have a nonempty solution set and turn out to be jointly-convex. To compute variational equilibria, we devise different first-order projection Tikhonov-like methods whose convergence properties are studied. We provide complexity bounds and we equip our analysis with numerical tests using real-world financial datasets.