  Online platforms, such as Airbnb, hotels.com, Amazon, Uber and Lyft, can
control and optimize many aspects of product search to improve the efficiency
of marketplaces. Here we focus on a common model, called the discriminatory
control model, where the platform chooses to display a subset of sellers who
sell products at prices determined by the market and a buyer is interested in
buying a single product from one of the sellers. Under the commonly-used model
for single product selection by a buyer, called the multinomial logit model,
and the Bertrand game model for competition among sellers, we show the
following result: to maximize social welfare, the optimal strategy for the
platform is to display all products; however, to maximize revenue, the optimal
strategy is to only display a subset of the products whose qualities are above
a certain threshold. We extend our results to Cournot competition model, and
show that the optimal search segmentation mechanisms for both social welfare
maximization and revenue maximization also have simple threshold structures.
The threshold in each case depends on the quality of all products, the
platform's objective and seller's competition model, and can be computed in
linear time in the number of products.
