Numerical approximation of Nash equilibria for a class of non-cooperative differential games

Abstract : In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of Hamilton-Jacobi equations. The numerical method is based on the Dynamic Programming Principle for every equation and on a global fixed point iteration. We present the numerical solutions of some two-player games in one and two dimensions. The paper has an experimental nature, but some features and properties of the approximation scheme are discussed.
Type de document :
Chapitre d'ouvrage
Leon Petrosjan and Vladimir Mazalov. Game Theory and Applications, 16, Nova Publishers, pp.45-58, 2013, 978-1-62618-444-2
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Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 14:45:16
Dernière modification le : jeudi 10 mai 2018 - 02:05:28

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  • HAL Id : hal-00724741, version 1
  • ARXIV : 1109.3569

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Simone Cacace, Emiliano Cristiani, Maurizio Falcone. Numerical approximation of Nash equilibria for a class of non-cooperative differential games. Leon Petrosjan and Vladimir Mazalov. Game Theory and Applications, 16, Nova Publishers, pp.45-58, 2013, 978-1-62618-444-2. 〈hal-00724741〉

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