TY  - JOUR
A1  - Campana, Francesca Calà
A1  - Ciaramella, Gabriele
A1  - Borzì, Alfio
T1  - Nash Equilibria and Bargaining Solutions of Differential Bilinear Games
JF  - Dynamic Games and Applications
N2  - 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.
KW  - bilinear evolution model
KW  - Nash equilibria
KW  - Nash bargaining problem
KW  - optimal control theory
KW  - quantum evolution models
KW  - Lotka-Volterra models
KW  - Newton methods
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-283897
VL  - 11
IS  - 1
ER  -