Dealer Competition Balancing Adverse Selection and Inventory Costs

Summary

This theoretical study analyzes how dealers set quotes when competing to handle a client's order flow. The client may trade based on private information, a desire to reduce idiosyncratic risk, or both. Dealers cannot observe the client's motive directly; they know only its probability distribution. Their quoting problem is therefore to balance losses from trading with an informed client against the costs of holding inventory.

The paper considers one-shot Nash competition among any number of identical dealers. It establishes that, under conditions described as essentially minimal, a unique symmetric equilibrium exists and can be characterized by solving a nonlinear ordinary differential equation. The abstract does not spell out those conditions, the equation, or numerical examples, so it offers a theoretical characterization rather than a practical quoting recipe or empirical test. Its framework is relevant to liquidity provision and market making, especially where order flow may reflect either information or risk management needs.

Key ideas

• Dealers compete in a one-shot Nash game to attract a client's order flow.
• The client may trade because of private information, idiosyncratic risk, or both.
• Dealers observe the distribution of client types but not the motive behind a particular trade.
• Quote schedules balance adverse-selection exposure against inventory costs.
• The symmetric equilibrium is unique under stated conditions and can be characterized with a nonlinear ordinary differential equation.

Tags

# Liquidity Provision with Adverse Selection and Inventory Costs


# 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 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.