  This paper constructs optimal brokerage contracts for multiple
(heterogeneous) clients trading a single asset whose price follows the
Almgren-Chriss model. The distinctive features of this work are as follows: (i)
the reservation values of the clients are determined endogenously, and (ii) the
broker is allowed to not offer a contract to some of the potential clients,
thus choosing her portfolio of clients strategically. We find a computationally
tractable characterization of the optimal portfolios of clients (up to a
digital optimization problem, which can be solved efficiently if the number of
potential clients is small) and conduct numerical experiments which illustrate
how these portfolios, as well as the equilibrium profits of all market
participants, depend on the price impact coefficients.
