Noisy Signalling in Financial Markets

Separating signaling equilibria of financial markets with anonymous insiders are investigated. Definitions of separating signaling equilibria are extended to allow for the noise that provides anonymity. The role of noise in equilibrium existence results is clarified. In particular, the result of Glosten and Madhavan, that noise is necessary for dealer markets to remain open, is qualified. The separating signaling equilibrium is written as the solution to a central planner's problem. Besides facilitating computation, this formulation highlights: (i) the critical nature of incentive compatibility constraints. (ii) the welfare aspects . The former causes many equilibrium price-quantity schedules to be non-linear and non-differentiable. An analysis of the latter leads to the conclusion that Pareto-efficient outcomes can be approximated by a repeated version of an insider game.