On The Existence of Linear Equilibria in Models of Market Making
2001, Mathematical Finance
Mark Bagnoli, S. Viswanathan, Craig W. Holden
We derive the necessary and sufficient conditions for a linear equilibrium in three types of competitive market making models: Kyle type models (when market makers only observe aggressive net order flow), Glosten-Milgrom and Easley-O'Hara type models (when market makers observe and trade one order at a time), and call markets models (individual orders 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 distribution 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 we provide a large number of examples of linear equilibria for each of the models.
Bagnoli, Mark, S. Viswanathan, and Craig W. Holden (2001), “On The Existence of Linear Equilibria in Models of Market Making,” Mathematical Finance, Vol. 11, pp. 1-31.