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We study one-shot Nash competition between an arbitrary number of identicaldealers that compete for the order flow of a client. The client trades eitherbecause of proprietary information, exposure to idiosyncratic risk, or a mix ofboth trading motives. When quoting their price schedules, the dealers do notknow the client's type but only its distribution, and in turn choose theirprice quotes to mitigate between adverse selection and inventory costs. Underessentially minimal conditions, we show that a unique symmetric Nashequilibrium exists and can be characterized by the solution of a nonlinear ODE.

Liquidity Provision with Adverse Selection and Inventory Costs