Volume 26, 2020
|Number of page(s)||38|
|Published online||14 February 2020|
On Mean Field Games models for exhaustible commodities trade
Baylor University, Department of Mathematics,
One Bear Place #97328,
2 Univ Lyon, École centrale de Lyon, CNRS UMR 5208, Institut Camille Jordan, 36 Avenue Guy de Collonge, 69134 Ecully Cedex, France.
* Corresponding author: Jameson Graber@baylor.edu
Accepted: 14 February 2019
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.
Mathematics Subject Classification: 35Q91 / 60H30 / 35K61
Key words: Mean field games / exhaustible resources / Cournot models / Nash equilibrium
© EDP Sciences, SMAI 2020
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