Informed Trading with Oligopolistic Market Makers

Abstract

We study Kyle-type models with imperfect competition among market makers. In discrete time, we prove existence and uniqueness of linear equilibria both when the informed trader observes noise trades and when noise is not observable, and we obtain explicit convergence rates as the number of trading periods increases. To resolve the ill-posedness of prices in continuous time, we formulate equilibria in terms of belief dynamics and develop two continuous-time limits depending on admissibility: the finite-variation restriction on the informed trader’s strategy and the unrestricted case allowing a nonzero martingale component. We show that the continuous-time equilibria arise as sharp limits of their discrete-time counterparts, thereby providing an informational foundation for admissibility assumptions and clarifying how noise observability influences equilibrium behavior. Under imperfect competition, temporary price impact and negative autocorrelation arise, and admissibility shifts profits from the informed trader to market makers. Moreover, whether noise trades are observable or not affects equilibrium price impact and the informed trader’s ability to exploit private information.