ON MEAN FIELD GAMES MODELS FOR EXHAUSTIBLE COMMODITIES TRADE

P. Jameson Graber (1) , Charafeddine Mouzouni (2)

1 Baylor University
2 PSPM - Probabilités, statistique, physique mathématique

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 M1 topology, which is defined for distribution-valued processes.

Mots clés: mean field games; Nash equilibrium; Sokorokhod M1 topology; Cournot models; exhaustible resources

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

P. Jameson Graber, Charafeddine Mouzouni. ON MEAN FIELD GAMES MODELS FOR EXHAUSTIBLE COMMODITIES TRADE. ESAIM: Control, Optimisation and Calculus of Variations, In press, ⟨10.1051/cocv/2019008⟩. ⟨hal-01850147v3⟩