Algorithmic Information Design for Searchers with Uncertain Alternatives

Abstract

Advertisements reveal information to consumers who decide on further information acquisition and eventual purchase. Anderson and Renault (2006) first modeled this problem using an information-design framework where the advertiser acts as a sender and the consumer as a receiver. Due to search frictions and the consumer's outside option, search for additional information is not always worthwhile for the receiver. Thus, the sender's information design is used to make further search attractive and ultimately induce purchase. Following Lyu (2023), we study the optimal information design for a sender who sells search goods to a consumer with uncertain alternatives. Instead of making relaxations to the sender's problem (as done in Lyu, 2023), we work directly on the joint distribution over realized values and signals. Our contributions are twofold. First, we give a method, based on duality arguments, to verify whether a given information strategy is optimal. We illustrate the value of this verification framework in a competitive extension, where it certifies a non-trivial symmetric equilibrium for two senders with a common convex prior. Second, on the algorithmic front, we develop an FPTAS that finds for the seller a signaling scheme whose utility differs from that of the optimal solution by at most an additive $\epsilon$ error, for any $\epsilon > 0$.