Corpus ID: 208202006

Some analytically solvable problems of the mean-field games theory

@article{Nikulin2019SomeAS,
  title={Some analytically solvable problems of the mean-field games theory},
  author={S. I. Nikulin and O. Rozanova},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice of data, this problem can be reduced to solving a quadratically nonlinear system of ODEs. 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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