Information Design with Unknown Prior

TL;DR

This paper develops learning algorithms for information designers to infer receivers' prior beliefs from actions, achieving fast regret bounds and improving decision-making in uncertain environments.

Contribution

It introduces algorithms that learn receivers' priors from actions with tight regret bounds, enabling better information design without prior knowledge.

Findings

Achieves a regret bound of Θ(log T) in general cases.

Achieves a regret bound of Θ(log log T) for binary actions.

Algorithms perform near-optimally in learning priors from actions.

Abstract

Information designers, such as online platforms, often do not know the beliefs of their receivers. We design learning algorithms so that the information designer can learn the receivers' prior belief from their actions through repeated interactions. Our learning algorithms achieve no regret relative to the optimality for the known prior at a fast speed, achieving a tight regret bound $\Theta(\log T)$ in general and a tight regret bound $\Theta(\log \log T)$ in the important special case of binary actions.