Liquidity Provision with Adverse Selection and Inventory Costs
研究多个相同做市商竞争客户订单流时的定价策略，客户因私有信息或风险暴露而交易，做市商在不知客户类型下报价以平衡逆向选择和库存成本，证明存在唯一对称纳什均衡。
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 ordinary differential equation.