Nash Equilibria and Bargaining Solutions of Differential Bilinear Games

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2021
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Calà Campana, Francesca
Borzì, Alfio
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Dynamic Games and Applications. Birkhäuser. 2021, 11(1), pp. 1-28. ISSN 2153-0785. eISSN 2153-0793. Available under: doi: 10.1007/s13235-020-00351-2
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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.

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ISO 690CALÀ CAMPANA, Francesca, Gabriele CIARAMELLA, Alfio BORZÌ, 2021. Nash Equilibria and Bargaining Solutions of Differential Bilinear Games. In: Dynamic Games and Applications. Birkhäuser. 2021, 11(1), pp. 1-28. ISSN 2153-0785. eISSN 2153-0793. Available under: doi: 10.1007/s13235-020-00351-2
BibTex
@article{CalaCampana2021-03Equil-49235,
  year={2021},
  doi={10.1007/s13235-020-00351-2},
  title={Nash Equilibria and Bargaining Solutions of Differential Bilinear Games},
  number={1},
  volume={11},
  issn={2153-0785},
  journal={Dynamic Games and Applications},
  pages={1--28},
  author={Calà Campana, Francesca and Ciaramella, Gabriele and Borzì, Alfio},
  note={A Correction to this paper has been published: https://doi.org/10.1007/s13235-021-00394-z}
}
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A Correction to this paper has been published: https://doi.org/10.1007/s13235-021-00394-z
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