  We use a principal-agent model to analyze the structure of a book-driven
dealer market when the dealer faces competition from a crossing network or dark
pool. The agents are privately informed about their types (e.g. their
portfolios), which is something that the dealer must take into account when
engaging his counterparties. Instead of trading with the dealer, the agents may
chose to trade in a crossing network. We show that the presence of such a
network results in more types being serviced by the dealer and that, under
certain conditions and due to reduced adverse selection effects, the book's
spread shrinks. We allow for the pricing on the dealer market to determine the
structure of the crossing network and show that the same conditions that lead
to a reduction of the spread imply the existence of an equilibrium
book/crossing network pair.
