On the structure and existence of linear equilibria with a constrained trader

Abstract

We study a discrete-time Kyle model with a single constrained trader, competitive market makers, and noise traders. Within the linear class, we show that any equilibrium necessarily reduces to a representation based on two state variables: the market maker’s expectation of the trader’s remaining demand and the residual demand beyond this expectation. This result implies that the equilibrium structure adopted in the continuoustime constrained trader model of Choi et al. (2023) is not a particular modeling choice, but the only linear structure consistent with equilibrium in the discrete-time analogue. We also establish the existence of a linear equilibrium in this setting.