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

arXiv: https://arxiv.org/abs/1811.02811 · HTML: https://mlsanity.com/paper/1811.02811/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [Learning Discrete-Time Major-Minor Mean Field Games](https://mlsanity.com/paper/2312.10787/) (2023)

## Abstract (arXiv)

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.