  We study one-shot Nash competition between an arbitrary number of identical
dealers that compete for the order flow of a client. The client trades either
because of proprietary information, exposure to idiosyncratic risk, or a mix of
both trading motives. When quoting their price schedules, the dealers do not
know the client's type but only its distribution, and in turn choose their
price quotes to mitigate between adverse selection and inventory costs. Under
essentially minimal conditions, we show that a unique symmetric Nash
equilibrium exists and can be characterized by the solution of a nonlinear ODE.
