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Main Authors: Ferrari, Giorgio, Tzouanas, Ioannis
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.08317
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author Ferrari, Giorgio
Tzouanas, Ioannis
author_facet Ferrari, Giorgio
Tzouanas, Ioannis
contents In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an Itô diffusion via one-sided singular stochastic control, aiming to maximize a long-term average expected profit criterion. The mean-field interaction is of scalar type through the stationary distribution of the population. Due to the presence of uncertainty, the problem involves the study of a stochastic (zero-sum) game, where the decision maker chooses the "best" singular control policy, while the adversarial player selects the "worst" probability measure. Using a constructive approach, we prove existence and uniqueness of a stationary mean-field equilibrium. Finally, we present an example of mean-field optimal extraction of natural resources under uncertainty and we analyze the impact of uncertainty on the mean-field equilibrium.
format Preprint
id arxiv_https___arxiv_org_abs_2505_08317
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stationary Mean-Field Games of Singular Control under Knightian Uncertainty
Ferrari, Giorgio
Tzouanas, Ioannis
Optimization and Control
49L20, 91A07, 91A15, 91A16, 91A26, 9J15, 60J70, 35R35
In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an Itô diffusion via one-sided singular stochastic control, aiming to maximize a long-term average expected profit criterion. The mean-field interaction is of scalar type through the stationary distribution of the population. Due to the presence of uncertainty, the problem involves the study of a stochastic (zero-sum) game, where the decision maker chooses the "best" singular control policy, while the adversarial player selects the "worst" probability measure. Using a constructive approach, we prove existence and uniqueness of a stationary mean-field equilibrium. Finally, we present an example of mean-field optimal extraction of natural resources under uncertainty and we analyze the impact of uncertainty on the mean-field equilibrium.
title Stationary Mean-Field Games of Singular Control under Knightian Uncertainty
topic Optimization and Control
49L20, 91A07, 91A15, 91A16, 91A26, 9J15, 60J70, 35R35
url https://arxiv.org/abs/2505.08317