Nash Equilibria and Bargaining Solutions of Differential Bilinear Games

Artikel

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.

Objekt anzeigen

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Journal: Dynamic Games and Applications ; ISSN: 2153-0793 ; Volume: 11 ; Year: 2020 ; Issue: 1 ; Pages: 1-28 ; New York, NY: Springer US

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Economics of Minorities, Races, Indigenous Peoples, and Immigrants; Non-labor Discrimination ; Economic History: Transport, International and Domestic Trade, Energy, Technology, and Other Services: General, International, or Comparative ; IT Management ; Energy: Demand and Supply; Prices
• Thema: Bilinear evolution models ; Nash equilibria ; Nash bargaining problem ; Optimal control theory ; Quantum evolution models ; Lotka–Volterra models ; Newton methods

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Calà Campana, Francesca ; Ciaramella, Gabriele ; Borzì, Alfio
• Ereignis: Veröffentlichung
• (wer): Springer US
• (wo): New York, NY
• (wann): 2020

Weitere Informationen

• DOI: doi:10.1007/s13235-020-00351-2