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.
Cardaliaguet, P., Cirant, M., Porretta, A. (2020). Remarks on Nash equilibria in mean field game models with a major player. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148(10), 4241-4255 [10.1090/proc/15135].
Remarks on Nash equilibria in mean field game models with a major player
Porretta, A
2020-01-01
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.| File | Dimensione | Formato | |
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