Mean field games equations with quadratic Hamiltonian: a specific approach

Olivier Guéant

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arXiv · 1106.3269

Mean field games equations with quadratic Hamiltonian: a specific approach

Olivier Guéant

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Abstract

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the mean field games (MFG) equations into a system of simpler coupled partial differential equations, in the case of a quadratic Hamiltonian. This system is then used to exhibit a monotonic scheme to build solutions of the MFG equations. Effective numerical methods based on this constructive scheme are presented and numerical experiments are carried out.

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Olivier Guéant. 2011-06-16. Mean field games equations with quadratic Hamiltonian: a specific approach. https://arxiv.org/abs/1106.3269

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