Pré-Publication, Document De Travail Année : 2011

Mean field games equations with quadratic Hamiltonian: a specific approach

Résumé

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to +∞, have been introduced by J.-M. Lasry and P.-L. Lions in [11, 12, 13]. 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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hal-00628536 , version 1 (03-10-2011)

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  • HAL Id : hal-00628536 , version 1

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Olivier Guéant. Mean field games equations with quadratic Hamiltonian: a specific approach. 2011. ⟨hal-00628536⟩
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