# Linear Quadratic Mean Field Games with Quantile-Dependent Cost Coefficients

arXiv: https://arxiv.org/abs/2411.01668 · HTML: https://mlsanity.com/paper/2411.01668/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2024.

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

- [Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning](https://mlsanity.com/paper/2602.14339/) (2026)

## Abstract (arXiv)

This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population's state distribution through its quantile function. Such a formulation allows for modelling agents that are sensitive to not only the population average but also the population variance. The corresponding mean field game equilibrium is identified, which involves solving two coupled differential equations: one is a Riccati equation and the other the variance evolution equation. Furthermore, the conditions for the existence and uniqueness of the mean field equilibrium are established. Finally, numerical results are presented to illustrate the behavior of two coupled differential equations and the performance of the mean field game solution.