# Price of Anarchy for Mean Field Games

arXiv: https://arxiv.org/abs/1802.04644 · HTML: https://mlsanity.com/paper/1802.04644/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Convergence of Actor-Critic Learning for Mean Field Games and Mean Field Control in Continuous Spaces](https://mlsanity.com/paper/2511.06812/) (2025)

## Abstract (arXiv)

The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in routing games, is extended to mean field games. The price of anarchy is defined as the ratio of a worst case social cost computed for a mean field game equilibrium to the optimal social cost as computed by a central planner. We illustrate properties of such a price of anarchy on linear quadratic extended mean field games, for which explicit computations are possible. Various asymptotic behaviors of the price of anarchy are proved for limiting behaviors of the coefficients in the model and numerics are presented.