The Limits of Search Algorithms

Abstract: A platform commits to a search algorithm that maps prices to search order. Given this algorithm, sellers set prices, and consumers engage in sequential search. This framework generalizes the ordered search literature. We introduce a special class of search algorithms, termed ''contracts,'' show that they implement all possible equilibrium prices and then characterize the set of implementable prices. Within this set, we identify the seller-optimal contract, whose first-best outcome remains an open problem for a multiproduct seller. Our findings highlight the conditions under which the platform favors price dispersion or price symmetry. Furthermore, we characterize the consumer-optimal and socially optimal contracts, which exert opposing forces to the seller-optimal contract: while the seller-optimal contract promotes higher prices, the consumer-optimal and socially optimal contracts favor lower prices.