Geodesic
Price of anarchy for Mean Field Games
René Carmona1 ; Christy V. Graves2 ; Zongjun Tan3
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
ESAIM. Proceedings, Tome 65 (2019), pp. 349-383.

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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.
DOI : 10.1051/proc/201965349

René Carmona 1 ; Christy V. Graves 2 ; Zongjun Tan 3

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 
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     author = {Ren\'e Carmona and Christy V. Graves and Zongjun Tan},
     title = {Price of anarchy for {Mean} {Field} {Games}},
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René Carmona; Christy V. Graves; Zongjun Tan. Price of anarchy for Mean Field Games. ESAIM. Proceedings, Tome 65 (2019), pp. 349-383. doi : 10.1051/proc/201965349. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965349/

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