A company selling a product to a stream of customers usually sets a single price and only sees if each customer buys. This limited feedback makes it hard to learn the optimal price, leading to a regret (lost revenue) that scales with T raised to the 2/3 power. Instead of one price, a menu of two options, like two subscription levels, can be offered. Each option gives the product with some probability at some expected payment. With just two options, the seller can learn almost as much as if customers revealed their exact willingness to pay. This reduces regret to the square root of T, a large improvement. The result holds for any unknown customer value distribution, meaning companies can get near-optimal revenue without needing complex market research or many choices.
Sellers can match unlimited menus with just two purchase options
Dai, Lin and Slivkins prove that two randomized purchase options match the learning performance of unlimited menus, up to logarithmic factors.
Big Tech
Yan Dai · Tao Lin · Aleksandrs Slivkins
Massachusetts Institute of Technology · Microsoft Research New England · The Chinese University of Hong Kong, Shenzhen · Microsoft Research NYC
Research Digest··3 min read
In one line
Two menu options in dynamic pricing achieve the same regret as infinite menus, up to logarithmic factors.
Read it as
A seller learning what customers will pay can do substantially better by offering two purchase options rather than one posted price.
The authors study a seller with unlimited inventory facing a sequence of customers whose values are drawn independently from the same unknown distribution.
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