Robustness of equilibrium in the Kyle model of informed speculation

Annals of Finance. 2015. P. 297–318.

Boulatov A., Bernhardt D.

We analyze a static Kyle (Continuous auctions and insider trading. Princeton University, Princeton, 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. © 2015 Springer-Verlag Berlin Heidelberg

Keywords: market microstructure, robustness, uniqueness, Bayesian Nash equilibrium, Information, Informed speculation

Publication based on the results of: Research in Financial Economics: International Capital Flows, Efficiency of Financial Markets and Corporate Governance (2015)