Liquidity Provision with Adverse Selection and Inventory Costs

TL;DR

This paper analyzes a model of multiple dealers competing for client order flow, balancing adverse selection and inventory costs, and characterizes the unique symmetric Nash equilibrium through a nonlinear differential equation.

Contribution

It introduces a novel equilibrium characterization for dealer competition considering adverse selection and inventory costs in a one-shot game.

Findings

Existence of a unique symmetric Nash equilibrium.

Equilibrium characterized by a nonlinear ODE.

Insights into dealer pricing strategies under uncertainty.

Abstract

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.