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.

q-deformations offer a systematic way to generalize familiar mathematical structures, revealing hidden symmetries and richer geometries that collapse back to classical frameworks as the deformation parameter goes to 1. Beyond their mathematical elegance, q-deformations have naturally emerged in diverse areas of theoretical physics, offering fresh perspectives on quantization, regularization, and non-commutative geometry. In this talk, we will explore how q-deformations intersect with the intriguing question of the uniqueness of string scattering amplitudes.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.