Following Kamenica and Gentzkow, this paper studies persuasion as an information design problem. We investigate how mistakes in probabilistic inference impact optimal persuasion. The concavification method is shown to extend naturally to a large class of belief updating rules, which we identify and characterize. This class comprises many non-Bayesian models discussed in the literature. We apply this new technique to gain insight into the revelation principle, the ranking of updating rules, when persuasion is beneficial to the sender, and when it is detrimental to the receiver. Our key result also extends to shed light on the question of robust persuasion.

Consumers purchase multiple types of goods but may be able to examine only a limited number of markets for the best price. We propose a simple model that captures these features, conveying new insights. A firm’s price can deflect or draw attention to its market, and consequently, limited attention introduces a new dimension of cross-market competition. We characterize the equilibrium and show that having partially attentive consumers improves consumer welfare. With less attention, consumers are more likely to miss the best offers; but enhanced cross-market competition decreases average price paid, as leading firms try to stay under the consumers’ radar.