English

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

Numerical Analysis 2016-02-19 v1 Systems and Control Analysis of PDEs Optimization and Control

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.

Keywords

Cite

@article{arxiv.1109.3569,
  title  = {Numerical approximation of Nash equilibria for a class of non-cooperative differential games},
  author = {Simone Cacace and Emiliano Cristiani and Maurizio Falcone},
  journal= {arXiv preprint arXiv:1109.3569},
  year   = {2016}
}