| Issue |
ESAIM: ProcS
Volume 65, 2019
CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|
|
|---|---|---|
| Page(s) | 349 - 383 | |
| DOI | https://doi.org/10.1051/proc/201965349 | |
| Published online | 02 April 2019 | |
Price of anarchy for Mean Field Games
1
Operations Research and Financial Engineering, Princeton University, Partially supported by NSF #DMS-1716673 and ARO #W911NF-17-1-0578
2
Program in Applied and Computational Mathematics, Princeton University, Partially supported by NSF #DMS-1515753 and NSF GRFP
3
Operations Research and Financial Engineering, Princeton University, Partially supported by NSF #DMS-1515753
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. A sufficient and necessary condition to have no price of anarchy is presented. Various asymptotic behaviors of the price of anarchy are proved for limiting behaviors of the coefficients in the model and numerics are presented.
© EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.