Liquidity Provision with Adverse Selection and Inventory Costs

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