Flexible Information Acquisition in the Kyle Model

TL;DR

This paper analyzes how an informed trader optimally acquires costly information in the Kyle model, showing that continuous signals are optimal and that the distribution of signals can be simplified without loss, affecting trading outcomes.

Contribution

It introduces an entropy-based cost model for information acquisition and demonstrates the optimality of continuous, normally distributed signals in the Kyle equilibrium.

Findings

Continuous signals are optimal regardless of prior.

Any continuous signal yields the same ex-ante value and trading distribution.

Increasing acquisition costs reduces profit potential and information leakage.

Abstract

We study an information acquisition problem in which an informed trader acquires costly information prior to trading in the Kyle equilibrium. The cost of information acquisition is represented by an entropy cost. Regardless of the prior distribution of the asset payoff, continuous signals are optimal. Moreover, any continuously distributed signal, together with an associated logit type posterior distribution of the payoff, yields the same ex-ante value for the informed trader, the same distribution of posterior expected payoff, and the same unconditional distribution of the informed trader's trading strategy. Consequently, a normally distributed signal can be adopted without loss of generality. We further show that when the information acquisition cost increases or the volatility of noise trades decreases, the variance of the posterior expected payoff declines, the profit potential from trading diminishes, meanwhile the posterior expected payoff increasingly resembles a normal distribution, and the information leakage cost from trading decreases.