Remarks on Nash equilibria in mean field game models with a major player

Cardaliaguet, P.; Cirant, M.; Porretta, A.

doi:10.1090/proc/15135

Remarks on Nash equilibria in mean field game models with a major player
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by P. Cardaliaguet, M. Cirant and A. Porretta

Proc. Amer. Math. Soc. 148 (2020), 4241-4255

DOI: https://doi.org/10.1090/proc/15135

Published electronically: July 20, 2020

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Abstract:

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then, for games with a finite number $N$ of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as $N$ tends to infinity.

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