A mean-field model of optimal investment

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 690

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods ; Optimization Techniques; Programming Models; Dynamic Analysis ; Existence and Stability Conditions of Equilibrium ; Noncooperative Games ; Intertemporal Firm Choice: Investment, Capacity, and Financing ; Market Structure, Pricing, and Design: Perfect Competition
• Subject: mean-field games ; mean-field equilibrium ; forward-backward ODEs ; optimal investment ; price formation

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Calvia, Alessandro ; Federico, Salvatore ; Ferrari, Giorgio ; Gozzi, Fausto
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2024

Further information

• URN: urn:nbn:de:0070-pub-29883840
• Last update: 10.03.2025, 11:46 AM CET