Geodesic
On certain analytically solvable problems of mean field games theory
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 3-11

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We study the mean field games equations consisting of the coupled Kolmogorov–Fokker–Planck and Hamilton–Jacobi–Bellman equations. The equations are supplemented with initial and terminal conditions. It is shown that for a certain specific choice of data this problem can be reduced to solving a quadratically nonlinear ODE system. This situation occurs naturally in economic applications. As an example, the problem of forming an investor's opinion on an asset is considered. 
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     author = {S. I. Nikulin and O. S. Rozanova},
     title = {On certain analytically solvable problems of mean field games theory},
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S. I. Nikulin; O. S. Rozanova. On certain analytically solvable problems of mean field games theory. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 3-11. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a0/