Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/289847 
Year of Publication: 
2024
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 690
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study.
Subjects: 
mean-field games
mean-field equilibrium
forward-backward ODEs
optimal investment
price formation
JEL: 
C02
C61
C62
C72
D25
D41
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Working Paper

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