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Published in: Dynamic Games and Applications 1/2021

Open Access 30-03-2020

Nash Equilibria and Bargaining Solutions of Differential Bilinear Games

Authors: Francesca Calà Campana, Gabriele Ciaramella, Alfio Borzì

Published in: Dynamic Games and Applications | Issue 1/2021

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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.

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Metadata
Title
Nash Equilibria and Bargaining Solutions of Differential Bilinear Games
Authors
Francesca Calà Campana
Gabriele Ciaramella
Alfio Borzì
Publication date
30-03-2020
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 1/2021
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-020-00351-2

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