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.
