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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\u2019 objectives with respect to the Nash equilibria. Results of numerical experiments successfully demonstrate the effectiveness of the proposed NE and NB computational framework.<\/jats:p>","DOI":"10.1007\/s13235-020-00351-2","type":"journal-article","created":{"date-parts":[[2020,3,30]],"date-time":"2020-03-30T19:12:31Z","timestamp":1585595551000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Nash Equilibria and Bargaining Solutions of Differential Bilinear Games"],"prefix":"10.1007","volume":"11","author":[{"given":"Francesca","family":"Cal\u00e0 Campana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriele","family":"Ciaramella","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alfio","family":"Borz\u00ec","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,3,30]]},"reference":[{"key":"351_CR1","volume-title":"Sobolev spaces","author":"RA Adams","year":"2003","unstructured":"Adams RA, Fournier J (2003) Sobolev spaces, 2nd edn. 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