The Strategy of Experts for Repeated Predictions

TL;DR

This paper examines how strategic experts should optimally reveal information over time when making repeated predictions, showing that truth-telling and updating with new signals is optimal, and analyzing the expected rewards in such settings.

Contribution

It extends prior work by analyzing repeated predictions with revisions, demonstrating that truth-telling and updating with new signals is optimal for experts.

Findings

Experts should always tell the truth when revising predictions.

Experts make a new prediction whenever they acquire a new signal.

The paper characterizes the expected total reward and its asymptotic behavior.

Abstract

We investigate the behavior of experts who seek to make predictions with maximum impact on an audience. At a known future time, a certain continuous random variable will be realized. A public prediction gradually converges to the outcome, and an expert has access to a more accurate prediction. We study when the expert should reveal his information, when his reward is based on a proper scoring rule (e.g., is proportional to the change in log-likelihood of the outcome). In Azar et. al. (2016), we analyzed the case where the expert may make a single prediction. In this paper, we analyze the case where the expert is allowed to revise previous predictions. This leads to a rather different set of dilemmas for the strategic expert. We find that it is optimal for the expert to always tell the truth, and to make a new prediction whenever he has a new signal. We characterize the expert's expectation for his total reward, and show asymptotic limits