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Working paper

Robustness of equilibrium in the Kyle model of informed speculation

Bernhardt D., Boulatov A.
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. We also establish that if a non-linear equilibrium exists, then it is not robust.