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

@article{Cardaliaguet2018RemarksON,
  title={Remarks on Nash equilibria in mean field game models with a major player},
  author={Pierre Cardaliaguet and Marco Cirant and Alessio Porretta},
  journal={arXiv: Optimization and Control},
  year={2018}
}
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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