Macroscopic Market Making Games

ABSTRACT Building on the macroscopic market making framework as a control problem, this paper investigates its extension to stochastic games. In the context of price competition, each agent is benchmarked against the best quote offered by the others. We begin with the linear case. While constructing the solution directly, the ordering property and the dimension reduction in the equilibrium are revealed. For the nonlinear case, we extend the decoupling approach by introducing a multidimensional characteristic equation to analyze the well‐posedness of the forward–backward stochastic differential equations. Properties of the coefficients in this characteristic equation are derived using tools from nonsmooth analysis. Several new well‐posedness results are presented. Finally, we discuss applications to price impacts and the optimal execution problem.