# Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

arXiv: https://arxiv.org/abs/1607.02130 · HTML: https://mlsanity.com/paper/1607.02130/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2016.

## Built on by (most cited first, 6 of 6)

- [Convergence of policy gradient methods for finite-horizon exploratory linear-quadratic control problems](https://mlsanity.com/paper/2211.00617/) (2022)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations](https://mlsanity.com/paper/2604.27372/) (2026)
- [Continuous Q-Score Matching: Diffusion Guided Reinforcement Learning for Continuous-Time Control](https://mlsanity.com/paper/2510.17122/) (2025)
- [Population-Aware Imitation Learning in Mean-field Games with Common Noise](https://mlsanity.com/paper/2605.03357/) (2026)

## Abstract (arXiv)

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources. Keywords: mean field type control, mean field games, linear-quadratic, optimal control, riccati equations, exhaustible resource production