Flexible Learning via Noise Reduction

Abstract

We develop a novel framework for costly information acquisition in which a decision-maker learns about an unobserved state by choosing a signal distribution, with the cost of information determined by the distribution of noise in the signal. We show that a natural set of axioms admits a unique integral representation of the cost function, and we establish the uniform dominance principle: there always exists an optimal experiment that generates signals with uniform noise. The uniform dominance principle allows us to reduce the infinite-dimensional optimization problem of finding an optimal information structure to finding a single parameter that measures the level of noise. We show that an optimal experiment exists under natural conditions, and we characterize it using generalized first-order conditions that accommodate non-smooth payoff functions and decision rules. Finally, we demonstrate the tractability of our framework in a bilateral trade setting in which a buyer learns about product quality.