Mean field games: numerical methods

Yves Achdou
Université de Paris VII (Denis Diderot) et Université de Paris VI (Pierre et Marie Curie)

Mean field type models describing the limiting behavior of differential game problems as the number of players
tends to infinity have recently been introduced by J-M. Lasry and P-L. Lions.
The main assumptions are that all the players are identical and that each player chooses his optimal strategy in view of
a global (partial) information on the game. At the limit a system of two coupled equations is obtained:
a forward in time Hamilton-Jacobi-Bellman for a value function and a backward in time Fokker-Planck equation for a probability measure.
Uniqueness is obtained under some reasonable assumptions. Infinite horizon games can also be considered.

This talk is focused on numerical methods for these models. Both finite and infinite horizon problems will be discussed.
Discrete optimal planning problems in the context of mean field games will be considered too.

Presentation (PDF File)

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