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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.
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https://hal.inria.fr/hal-00724741
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, August 22, 2012 - 2:45:16 PM
Last modification on : Thursday, March 5, 2020 - 6:23:17 PM

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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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