Persuasive Prediction via Decision Calibration
Jingwu Tang, Jiahao Zhang, Fei Fang, Zhiwei Steven Wu
TL;DR
This paper studies persuasive prediction, a data-driven, prior-free variant of Bayesian persuasion designed for large or infinite state spaces where the prior is unavailable. It introduces decision calibration as a behavioral model for receivers and develops an oracle-efficient minimax algorithm (PerDecCal) that learns decision-calibrated predictors from data to maximize the sender’s utility. In the single-receiver setting, the method achieves a Bayes-optimal benchmark within the class of predictors induced by the chosen hypothesis family, and the framework extends to stochastic (quantal) responses and infinite hypothesis classes via SmPerDecCal. The work provides finite-sample guarantees, shows no-regret properties for receivers under calibration, and establishes a principled bridge between calibration concepts and Bayesian persuasion, with practical implications for data-driven information design in complex environments.
Abstract
Bayesian persuasion, a central model in information design, studies how a sender, who privately observes a state drawn from a prior distribution, strategically sends a signal to influence a receiver's action. A key assumption is that both sender and receiver share the precise knowledge of the prior. Although this prior can be estimated from past data, such assumptions break down in high-dimensional or infinite state spaces, where learning an accurate prior may require a prohibitive amount of data. In this paper, we study a learning-based variant of persuasion, which we term persuasive prediction. This setting mirrors Bayesian persuasion with large state spaces, but crucially does not assume a common prior: the sender observes covariates $X$, learns to predict a payoff-relevant outcome $Y$ from past data, and releases a prediction to influence a population of receivers. To model rational receiver behavior without a common prior, we adopt a learnable proxy: decision calibration, which requires the prediction to be unbiased conditioned on the receiver's best response to the prediction. This condition guarantees that myopically responding to the prediction yields no swap regret. Assuming the receivers best respond to decision-calibrated predictors, we design a computationally and statistically efficient algorithm that learns a decision-calibrated predictor within a randomized predictor class that optimizes the sender's utility. In the commonly studied single-receiver case, our method matches the utility of a Bayesian sender who has full knowledge of the underlying prior distribution. Finally, we extend our algorithmic result to a setting where receivers respond stochastically to predictions and the sender may randomize over an infinite predictor class.