Persuasion and Incentives Through the Lens of Duality

TL;DR

This paper extends duality methods from mechanism design to persuasion, analyzing optimal schemes with or without payments, providing structural insights and simple characterizations in various settings.

Contribution

It introduces a duality-based framework for persuasion, including payment integration, and offers new structural results and tractable solutions for complex persuasion problems.

Findings

Duality provides simple characterizations of optimal persuasion schemes.

Payments enhance the persuasion power and are incorporated into the framework.

Structural insights are obtained for both single and multi-receiver settings.

Abstract

Lagrangian duality underlies both classical and modern mechanism design. In particular, the dual perspective often permits simple and detail-free characterizations of optimal and approximately optimal mechanisms. This paper applies this same methodology to a close cousin of traditional mechanism design, one which shares conceptual and technical elements with its more mature relative: the burgeoning field of persuasion. The dual perspective permits us to analyze optimal persuasion schemes both in settings which have been analyzed in prior work, as well as for natural generalizations which we are the first to explore in depth. Most notably, we permit combining persuasion policies with payments, which serve to augment the persuasion power of the scheme. In both single and multi-receiver settings, as well as under a variety of constraints on payments, we employ duality to obtain structural insights, as well as tractable and simple characterizations of optimal policies.