Addressing Hierarchical Jointly Convex Generalized Nash Equilibrium Problems with Nonsmooth Payoffs
研究了一种分层结构的广义纳什均衡问题，其中联合可行域由另一个纳什博弈的解集隐式定义，考虑了非光滑项以促进解的稀疏性，并设计了投影Tikhonov类方法求解，在真实金融数据集上进行了数值测试。
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.