Stationary Ergodic Mean-field Games of Constrained Singular Controls
Abstract
We study a stationary ergodic mean-field game of scalar type where the representative player controls a diffusion through two-sided singular controls exerted only at the jump times of an independent Poisson process. For each mean-field parameter, we solve the novel constrained ergodic singular control problem, proving that the optimal policy is of threshold type: the diffusion is reset at Poisson arrival times to the nearest boundary point of an interval. Our explicit probabilistic derivation of the stationary distributions induced by Poissonian threshold singular controls is a key contribution of independent interest. This distribution is used to construct the mean-field fixed-point map. We prove existence and uniqueness of the stationary mean-field equilibrium by combining the stationary density with the monotonicity and continuity of the optimal thresholds in the mean-field parameter. The model provides a tractable framework for a case study of partially reversible investment with singular adjustments under exogenous intervention constraints.
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BibTeX
@misc{ferrari2026stationary,
title = {{Stationary Ergodic Mean-field Games of Constrained Singular Controls}},
author = {Giorgio Ferrari and Jukka Lempa and Neofytos Rodosthenous and Harto Saarinen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13544},
eprint = {2610.13544},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13544},
}
RIS
TY - UNPB
TI - Stationary Ergodic Mean-field Games of Constrained Singular Controls
AU - Giorgio Ferrari
AU - Jukka Lempa
AU - Neofytos Rodosthenous
AU - Harto Saarinen
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13544
UR - https://arxiv.org/abs/2610.13544
AB - We study a stationary ergodic mean-field game of scalar type where the representative player controls a diffusion through two-sided singular controls exerted only at the jump times of an independent Poisson process. For each mean-field parameter, we solve the novel constrained ergodic singular control problem, proving that the optimal policy is of threshold type: the diffusion is reset at Poisson arrival times to the nearest boundary point of an interval. Our explicit probabilistic derivation of the stationary distributions induced by Poissonian threshold singular controls is a key contribution of independent interest. This distribution is used to construct the mean-field fixed-point map. We prove existence and uniqueness of the stationary mean-field equilibrium by combining the stationary density with the monotonicity and continuity of the optimal thresholds in the mean-field parameter. The model provides a tractable framework for a case study of partially reversible investment with singular adjustments under exogenous intervention constraints.
ER -