Persuading Skeptics and Fans in the Presence of Additional Information

Abstract

We consider the information design problem of a demand-maximizing firm launching a product of unknown quality to a polarized market consisting of customers who have heterogeneous prior beliefs about quality. The firm's information is publicly observable by all customers who can subsequently opt to acquire additional information at a cost from sources outside of the firm's control. Our study is motivated by the common practice of firms selectively soliciting expert opinion leaders to review a new product to inform potential customers about its quality. To analyze this problem, we construct a game-theoretic model of Bayesian persuasion between the firm and its customers. We characterize the firm's optimal information policy and show that it might exaggerate the product’s quality or release incomplete information about quality depending on the market characteristics. We delineate the impact of market heterogeneity and access to additional information on the informativeness of the firm’s policy, its expected demand, and the customers' expected utility. Our analysis surfaces conditions under which the information disseminated by the firm is likely to be less accurate, and when this can lead to reduced customer utility and social welfare. We discuss the implications of these results for the firm and policy makers.

Keywords: Information Design, Bayesian Persuasion, Costly Information Acquisition, Polarization, Product Reviews