On uniqueness of equilibrium in the Kyle model
The authors consider optimal trading for an informed investor in the Kyle model. It is assumed that the informed investor has knowledge of the true value of a firm, \(V\). The market maker observes the demand from the informed investor, \(D\), and of an uninformed one, \(U\). In the equilibrium the profit of the market maker is equal to zero. The problem of the informed investor is to find the best response function \(D=\phi(V)\) which maximizes his profit. The value of the firm and the demand of the uninformed investor are assumed to be independent normal variables: \(V\sim N(\mu, \sigma^2_V)\), \(U\sim N(0, \sigma^2_U)\). This problem was already considered in the literature and it was shown that in the class of affine functions the best response is \(\varphi(V) = (V-\mu)\sqrt{\sigma^2_U/\sigma^2_V}\). The authors of the article show that the same result holds for a broader class of response functions. In particular, the main result states that if the equilibrium best-response function \(\phi\) is an analytic function of an open connected interval that has maximal analytic extension, then it is an affine function.
scientific article; zbMATH DE number 6692618
scientific article