Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/288692 
Erscheinungsjahr: 
2020
Quellenangabe: 
[Journal:] Dynamic Games and Applications [ISSN:] 2153-0793 [Volume:] 11 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 1-28
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
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.
Schlagwörter: 
Bilinear evolution models
Nash equilibria
Nash bargaining problem
Optimal control theory
Quantum evolution models
Lotka–Volterra models
Newton methods
JEL: 
J15
N70
M15
Q41
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