  The modeling of the limit order book is directly related to the assumptions
on the behavior of real market participants. This paper is twofold. We first
present empirical findings that lay the ground for two improvements to these
models.The first one is concerned with market participants by adding the
additional dimension of informed market makers, whereas the second, and maybe
more original one, addresses the race in the book between informed traders and
informed market makers leading to different shapes of the order book.
  Namely we build an agent-based model for the order book with four types of
market participants: informed trader, noise trader, informed market makers and
noise market makers. We build our model based on the Glosten-Milgrom approach
and the most recent Huang-Rosenbaum-Saliba approach. We introduce a parameter
capturing the race between informed liquidity traders and suppliers after a new
information on the fundamental value of the asset. We then derive the whole
'static' limit order book and its characteristics -- namely the bid-ask spread
and volumes available at each level price -- from the interactions between the
agents and compare it with the pre-existing model. We then discuss the case
where noise traders have an impact on the fundamental value of the asset and
extend the model to take into account many kinds of informed market makers.
