Flexible Information Acquisition in the Kyle Model

2026-03-23

AI Summary

This study investigates how an informed trader optimally acquires information in the Kyle model when information acquisition entails entropy-based costs. Under an arbitrary prior distribution of asset payoff, it is shown that continuous signals are optimal, and all such signals are ex ante equivalent for the trader in terms of expected value, posterior payoff distribution, and unconditional strategy distribution, provided they induce the same posterior structure. The paper innovatively demonstrates that a Gaussian signal can represent any continuous signal without loss of generality. Furthermore, it establishes quantitative relationships among information cost, noise-trader volatility, posterior distribution shape, and information leakage cost: higher information costs or lower noise-trader volatility reduce posterior payoff variance and profit potential, drive the posterior toward normality, and simultaneously decrease information leakage costs.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Machine Learning: Information Theory
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Content-based information diffusion
• Security and Privacy: Large-scale security measurements

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.

Problem

• information acquisition
• Kyle model
• entropy cost
• informed trading
• signal distribution

Innovation

• entropy cost
• continuous signals
• Kyle model
• posterior distribution
• information acquisition