Liquidity Competition Between Brokers and an Informed Trader

ArXiv ID: 2503.08287 “View on arXiv”

Authors: Unknown

Abstract

We study a multi-agent setting in which brokers transact with an informed trader. Through a sequential Stackelberg-type game, brokers manage trading costs and adverse selection with an informed trader. In particular, supplying liquidity to the informed traders allows the brokers to speculate based on the flow information. They simultaneously attempt to minimize inventory risk and trading costs with the lit market based on the informed order flow, also known as the internalization-externalization strategy. We solve in closed form for the trading strategy that the informed trader uses with each broker and propose a system of equations which classify the equilibrium strategies of the brokers. By solving these equations numerically we may study the resulting strategies in equilibrium. Finally, we formulate a competitive game between brokers in order to determine the liquidity prices subject to precommitment supplied to the informed trader and provide a numerical example in which the resulting equilibrium is not Pareto efficient.

Keywords: Adverse Selection, Informed Trading, Stackelberg Game, Internalization-Externalization, Liquidity Supply, Equities (Market Microstructure)

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper presents a theoretical model with a complex Stackelberg game, PDEs, and a system of equilibrium equations that require numerical solving, indicating high math complexity. However, it focuses entirely on theoretical modeling and numerical simulation without presenting real-world backtests, datasets, or implementation details, placing it in the Lab Rats quadrant.
  flowchart TD
    A["Research Goal:<br>Model Broker Liquidity Supply<br>to an Informed Trader"] --> B["Methodology:<br>Multi-agent Sequential<br>Stackelberg Game"]
    B --> C["Key Inputs:<br>Informed Trader's Private<br>Signal & Asset Payoff"]
    C --> D["Process 1: Closed-Form Solution<br>Informed Trader's Strategy<br>with Brokers"]
    D --> E["Process 2: System of Equations<br>Classifying Broker<br>Equilibrium Strategies"]
    E --> F["Computation:<br>Numerical Solution of<br>Broker Competitive Game"]
    F --> G["Key Outcomes:<br>Equilibrium Liquidity Prices<br>& Pareto Inefficiency"]