  The latent order book of \cite{donier2015fully} is one of the most promising
agent-based models for market impact. This work extends the minimal model by
allowing agents to exhibit mean-reversion, a commonly observed pattern in real
markets. This modification leads to new order book dynamics, which we
explicitly study and analyze. Underlying our analysis is a mean-field
assumption that views the order book through its \textit{average} density. We
show how price impact develops in this new model, providing a flexible family
of solutions that can potentially improve calibration to real data. While no
closed-form solution is provided, we complement our theoretical investigation
with extensive numerical results, including a simulation scheme for the entire
order book.
