generalized nash equilibirum problems (gnep)

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

  • Lorenzo Lampariello
  • Simone Sagratella
  • Valerio Giuseppe Sasso
    • Categories Game Theory, Other Topics Tags , , , , ,

    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 … Read more

    Numerically tractable optimistic bilevel problems

  • Lorenzo Lampariello
  • Simone Sagratella
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Game Theory Tags , ,

    We consider fully convex lower level standard optimistic bilevel problems. We show that this class of mathematical programs is sufficiently broad to encompass significant real-world applications. We establish that the critical points of a relaxation of the original problem correspond to the equilibria of a suitably defined generalized Nash equilibrium problem. The latter game is … Read more