Competition in Dealer Markets with Internalisation and Externalisation

2026-06-04

AI Summary

This study investigates how multiple market makers balance internal hedging against external unwinding to manage inventory risk and maximize profits in the presence of competition for client order flow. By formulating a continuous-time dynamic quoting game and integrating stochastic control, calculus of variations, and game theory, the authors derive—for the first time—the closed-form Nash equilibrium in this setting. The analysis reveals that competition driven by externalization compels otherwise internalizing market makers to increase external trading, thereby raising aggregate hedging costs and significantly widening the bid–ask spreads faced by clients. This mechanism uncovers an endogenous source of liquidity deterioration in hybrid market-making environments, offering new insights into market maker behavior and the microstructure of financial markets.

Abstract

We model a market with multiple dealers who compete for client order flow by dynamically updating their bid and ask quotes for a risky asset. Dealers aim to maximise expected profits while controlling inventory risk by skewing their quotes to attract offsetting order flow (internalisation) or by directly offloading positions in the market (externalisation). Using a variational approach, we derive a closed-form equilibrium for the resulting Nash competition, shedding light on key features of dealer market dynamics. We show that dealers relying on internalisation are compelled to increase their externalisation activity when competing with externalising dealers. This strategic shift in equilibrium leads to significantly higher hedging costs for all dealers and substantially wider spreads for clients.

Problem

• Dealer Markets
• Internalisation
• Externalisation
• Inventory Risk
• Order Flow Competition

Innovation

• variational approach
• Nash equilibrium
• dealer competition
• internalisation
• externalisation