# Linear quadratic mean field games: Decentralized O(1/N)-Nash equilibria

arXiv: https://arxiv.org/abs/2107.09168 · HTML: https://mlsanity.com/paper/2107.09168/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2021.

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

- [MEMOA: Massive Mixtures of Online Agents via Mean-Field Decentralized Nash Equilibria](https://mlsanity.com/paper/2605.05492/) (2026)

## Abstract (arXiv)

This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The rescaling technique is further used for performance estimates, establishing an O(1/N)-Nash equilibrium for the obtained decentralized strategies.