Frequentist Persuasion

TL;DR

This paper analyzes how a sender's private experimentation influences persuasion when the decisionmaker learns from finite samples, showing convergence to Bayesian outcomes and revealing nonmonotonic effects of sample size on informativeness.

Contribution

It demonstrates that empirical payoff functions converge to Bayesian benchmarks under mild conditions and explores the nonmonotonic impact of sample size on optimal experiments.

Findings

Empirical payoffs hypo-converge to full-information payoffs.

Finite sample effects can increase or decrease informativeness.

An optimal finite sample size exists for many state-independent preference problems.

Abstract

A sender persuades a strategically naive decisionmaker (DM) by committing privately to an experiment. Sender's choice of experiment is unknown to the DM, who must form her posterior beliefs nonparametrically by applying some learning rule to an IID sample of (state, message) realizations. We show that, given mild regularity conditions, the empirical payoff functions hypo-converge to the full-information counterpart. This is sufficient to ensure that payoffs and optimal signals converge to the Bayesian benchmark. For finite sample sizes, the force of this "sampling friction" is nonmonotonic: it can induce more informative experiments than the Bayesian benchmark in settings like the classic Prosecutor-Judge game, and less revelation even in situations with perfectly aligned preferences. For many problems with state-independent preferences, we show that there is an optimal finite sample size for the DM. Although the DM would always prefer a larger sample for a fixed experiment, this result holds because the sample size affects sender's choice of experiment. Our results are robust to imperfectly informative feedback and the choice of learning rule.