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

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.

preprint2011arXivOpen access
Simone CacaceEmiliano CristianiMaurizio Falcone
Systems and Controlmath.APmath.OCmath.NA
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Simone CacaceEmiliano CristianiMaurizio Falcone

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