Existence and uniqueness results for a mean-field game of optimal investment

Alessandro Calvia, Salvatore Federico, Giorgio Ferrari and Fausto Gozzi

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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.

Date: 2024-04, Revised 2024-11
New Economics Papers: this item is included in nep-gth
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