Ergodic Problems for Second-Order Mean Field Games with State Constraints
Analysis of PDEs
2023-10-05 v1
Abstract
We study an ergodic mean field game problem with state constraints. In our model the agents are affected by idiosyncratic noise and use a (singular) feedback control to prevent the Brownian motion from exiting the domain. We characterize the equilibrium as the (possibly unique) solution to a second-order MFG system, where the value function blows up at the boundary while the density of the players is smooth and flattens near the boundary as a consequence of the singularity of the drift induced by the feedback strategy of the agents.
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Cite
@article{arxiv.2310.02652,
title = {Ergodic Problems for Second-Order Mean Field Games with State Constraints},
author = {Alessio Porretta and Michele Ricciardi},
journal= {arXiv preprint arXiv:2310.02652},
year = {2023}
}
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25 pages