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arXiv · 1109.3569

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

Simone Cacace·Emiliano Cristiani·Maurizio Falcone
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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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Simone Cacace, Emiliano Cristiani, Maurizio Falcone. 2011-09-16. Numerical approximation of Nash equilibria for a class of non-cooperative differential games. https://arxiv.org/abs/1109.3569

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