I am looking for a good introductory level textbook (or lecture notes) on mean field games that would be suitable for a graduate course. Ideally, it would include some brief words about optimal control and dynamic programming. Thanks!
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2 Answers
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The lecture notes on mean-field games of Lions, from a course at the Collège de France, have been typed out by Pierre Cardaliaguet. They address both optimal control and dynamic programming. I would think it will be hard to beat these for an authoritative exposition. For a summary of open problems you could look here.
answered Jul 7, 2021 at 17:13
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$\begingroup$ The second link is dead. The file can be found here: basepub.dauphine.psl.eu/handle/123456789/2263 or link.springer.com/article/10.1007/s11537-007-0657-8 In the future you may find it searching for "mean field games survey by Lasry and Lions" $\endgroup$– plmCommented Jan 20 at 5:24
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$\begingroup$ @plm --- thank you, I have fixed it. $\endgroup$ Commented Jan 20 at 7:46
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Here's my go to links:
PDE flavor notes by Ryzhik: https://math.stanford.edu/~ryzhik/STANFORD/MEAN-FIELD-GAMES/notes-mean-field.pdf
Probability flavor notes by Lacker: http://www.columbia.edu/~dl3133/MFGSpring2018.pdf
Background material on mean-field interacting processes by Golse: https://arxiv.org/abs/1301.5494
Books:
1). There is a two volume textbook "Probabilistic Theory of Mean Field Games with Applications " by Carmona and Delarue
2). A very comprehensive textbook on MFG is being written by Tamer Basar, but I don't know if it is ready yet.
answered Jul 7, 2021 at 17:33