Competitive Information Design in Sequential Search

Advertisements often strategically disclose information to consumers who make decisions on further information acquisition and eventual purchase. Anderson and Renault (2006) model this problem using an information design framework, where the advertiser acts as a sender and the consumer as a receiver. We extend this model to a competitive setting with horizontally differentiated senders competing for a unit-demand receiver. Under costly inspection, the receiver's optimal sequential search action is given by Weitzman's Index Algorithm. We give a method, based on duality arguments, to verify whether a sender's given information strategy constitutes a best response against his competitors (other senders). We establish the existence of an equilibrium in the game among senders when the prior distributions have no mass; we also illustrate that such equilibria may exhibit intricate behaviors. Finally, we meticulously characterize symmetric equilibria played by the senders for cases when the prior distributions have monotone increasing densities, while offering economic intuitions behind the insightful equilibrium structure.