@article{CampanaBorzi2022,
  author    = {Campana, Francesca Cal{\`a} and Borz{\`i}, Alfio},
  title     = {On the SQH Method for Solving Differential Nash Games},
  series = {Journal of Dynamical and Control Systems},
  volume    = {28},
  journal   = {Journal of Dynamical and Control Systems},
  issn      = {1573-8698},
  doi       = {10.1007/s10883-021-09546-1},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269111},
  pages     = {739-755},
  year      = {2022},
  abstract  = {A sequentialquadratic Hamiltonian schemefor solving open-loop differential Nash games is proposed and investigated. This method is formulated in the framework of the Pontryagin maximum principle and represents an efficient and robust extension of the successive approximations strategy for solving optimal control problems. Theoretical results are presented that prove the well-posedness of the proposed scheme, and results of numerical experiments are reported that successfully validate its computational performance.},
  language  = {en}
}
@article{CampanaCiaramellaBorzi2021,
  author    = {Campana, Francesca Cal{\`a} and Ciaramella, Gabriele and Borz{\`i}, Alfio},
  title     = {Nash Equilibria and Bargaining Solutions of Differential Bilinear Games},
  series = {Dynamic Games and Applications},
  volume    = {11},
  journal   = {Dynamic Games and Applications},
  number    = {1},
  doi       = {10.1007/s13235-020-00351-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-283897},
  pages     = {1-28},
  year      = {2021},
  abstract  = {This paper is devoted to a theoretical and numerical investigation of Nash equilibria and Nash bargaining problems governed by bilinear (input-affine) differential models. These systems with a bilinear state-control structure arise in many applications in, e.g., biology, economics, physics, where competition between different species, agents, and forces needs to be modelled. For this purpose, the concept of Nash equilibria (NE) appears appropriate, and the building blocks of the resulting differential Nash games are different control functions associated with different players that pursue different non-cooperative objectives. In this framework, existence of Nash equilibria is proved and computed with a semi-smooth Newton scheme combined with a relaxation method. Further, a related Nash bargaining (NB) problem is discussed. This aims at determining an improvement of all players' objectives with respect to the Nash equilibria. Results of numerical experiments successfully demonstrate the effectiveness of the proposed NE and NB computational framework.},
  language  = {en}
}