Information design for selling search goods and the effect of competition

I study optimal information provision by a search goods seller. While the seller controls a consumer's pre-search information, he cannot control post-search information because the consumer will inevitably learn the product's match after search. A relaxed problem approach is developed to solve the optimal design, which accommodates both continuous value distributions and ex-ante heterogeneous consumers with privately known outside options. The optimal design is shown to crucially depend on the outside option value distribution, and can be implemented by a simple upper-censorship signal under certain regularity conditions. Several applications are provided, including comparing information designs for search goods and experience goods, and studying the effect of competition with a large number of sellers.