Robustness of equilibrium in the Kyle model of informed speculation

Abstract

We analyze a static Kyle (1983) model in which a risk-neutral informed trader can use arbitrary (linear or non-linear) deterministic strategies, and a finite number of market makers can use arbitrary pricing rules. We establish a strong sense in which the linear Kyle equilibrium is robust: the first variation in any agent's expected payoff with respect to a small variation in his conjecture about the strategies of others vanishes at equilibrium. Thus, small errors in a market maker's beliefs about the informed speculator's trading strategy do not reduce his expected payoffs. Therefore, the original equilibrium strategies remain optimal and still constitute an equilibrium (neglecting the higher-order terms.) We also establish that if a non-linear equilibrium exists, then it is not robust. JEL Classification Numbers: G12, G14, C62.

Phase Transitions in Kyle's Model with Market Maker Profit Incentives

“…For any integrable functions f, g : R → R we define: Proof. From the independence of ṽ and ũ we have 2,x * = E (x * (ṽ) + ũ) 2 = E[x * (ṽ) 2 ] + σ 2 ũ.…”

“…Nishide [15] investigated a version of the model with competing market makers. Boulatov and Bernhardt [2] considered the robustness of the linear Kyle equilibrium with respect to small perturbations in the payoffs of the agents. Molino et al [9] studied the case where the market maker is setting the price of n correlated securities.…”