Strategic Learning and Trading in Broker-Mediated Markets (2412.20847v1)

Abstract: We study strategic interactions in a broker-mediated market. A broker provides liquidity to an informed trader and to noise traders while managing inventory in the lit market. The broker and the informed trader maximise their trading performance while filtering each other's private information; the trader estimates the broker's trading activity in the lit market while the broker estimates the informed trader's private signal. Brokers hold a strategic advantage over traders who rely solely on prices to filter information. We find that information leakage in the client's trading flow yields an economic value to the broker that is comparable to transaction costs; she speculates profitably and mitigates risk effectively, which, in turn, adversely impacts the informed trader's performance. In contrast, low signal-to-noise sources, such as prices, result in the broker's trading performance being indistinguishable from that of a naive strategy that internalises noise flow, externalises informed flow, and offloads inventory at a constant rate.