# Approximate Equilibrium Computation for Discrete-Time Linear-Quadratic Mean-Field Games

arXiv: https://arxiv.org/abs/2003.13195 · HTML: https://mlsanity.com/paper/2003.13195/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Classifying Ambiguous Identities in Hidden-Role Stochastic Games with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2210.12896/) (2022)
- [Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning](https://mlsanity.com/paper/2602.14339/) (2026)

## Abstract (arXiv)

While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy iteration algorithm for approximating the mean-field equilibrium in linear-quadratic MFGs with discounted cost. Given the mean-field, each agent faces a linear-quadratic tracking problem, the solution of which involves a dynamical system evolving in retrograde time. This makes the development of forward-in-time algorithm updates challenging. By identifying a structural property of the mean-field update operator, namely that it preserves sequences of a particular form, we develop a forward-in-time equilibrium computation algorithm. Bounds that quantify the accuracy of the computed mean-field equilibrium as a function of the algorithm's stopping condition are provided. The optimality of the computed equilibrium is validated numerically. In contrast to the most recent/concurrent results, our algorithm appears to be the first to study infinite-horizon MFGs with non-stationary mean-field equilibria, though with focus on the linear quadratic setting.