We investigate a mean field game model for the production of exhaustible resources. In this model, firms produce comparable goods, strategically set their production rate in order to maximise profit, and leave the market as soon as they deplete their capacities. We examine the related Mean Field Game system and prove well-posedness for initial measure data by deriving suitable a priori estimates. Then, we show that feedback strategies which are computed from the Mean Field Game system provide ε-Nash equilibria to the corresponding N-Player Cournot game, for large values of N. This is done by showing tightness of the empirical process in the Skorokhod M 1 topology, which is defined for distribution-valued processes.
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DOI : 10.1051/cocv/2019008
Mots-clés : Mean field games, exhaustible resources, Cournot models, Nash equilibrium
@article{COCV_2020__26_1_A11_0,
author = {Jameson Graber, Philip and Mouzouni, Charafeddine},
title = {On {Mean} {Field} {Games} models for exhaustible commodities trade},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019008},
mrnumber = {4064472},
zbl = {1437.35664},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019008/}
}
TY - JOUR AU - Jameson Graber, Philip AU - Mouzouni, Charafeddine TI - On Mean Field Games models for exhaustible commodities trade JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019008/ DO - 10.1051/cocv/2019008 LA - en ID - COCV_2020__26_1_A11_0 ER -
%0 Journal Article %A Jameson Graber, Philip %A Mouzouni, Charafeddine %T On Mean Field Games models for exhaustible commodities trade %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019008/ %R 10.1051/cocv/2019008 %G en %F COCV_2020__26_1_A11_0
Jameson Graber, Philip; Mouzouni, Charafeddine. On Mean Field Games models for exhaustible commodities trade. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 11. doi : 10.1051/cocv/2019008. http://www.numdam.org/articles/10.1051/cocv/2019008/
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