Mark Bagnoli
University of Michigan, Ann Arbor, MI 48109
S. Viswanathan
Duke University, Durham, NC 27708
Craig Holden
Indiana University, Bloomington, IN 47401
ABSTRACT
We derive necessary and sufficient conditions for a linear equilibrium in three types of competitive market making models: Kyle type models (when market makers only observe aggregate net order flow), Glosten-Milgrom and Easley-O'Hara type (GMEO, when market makers observe and trade one order at a time) and call markets (individual order models when market makers observe a number of orders before pricing and executing any of them). We study two cases-when privately informed (strategic) traders are symmetrically informed and when they have differential information. We derive necessary and sufficient conditions on the distributions of the random variables for a linear equilibrium. We also explore those features of the equilibrium that depend on linearity as opposed to the particular distributional assumptions, and provide a large number of examples of linear equilibria for each of the models.