Optimal and Robust Price Experimentation: Learning by Lottery

This paper studies optimal price learning for one or more items. We introduce the Schr\""odinger price experiment (SPE) which superimposes classical price experiments using lotteries, and thereby extracts more information from each customer interaction. If buyers are perfectly rational we show that there exist SPEs that in the limit of infinite superposition learn optimally \emphand exploit optimally. We refer to the new resulting mechanism as the hopeful mechanism (HM) since although it is incentive compatible, buyers can deviate with extreme consequences for the seller at very little cost to themselves. For real-world settings we propose a robust version of the approach which takes the form of a Markov decision process where the actions are functions. We provide approximate policies motivated by the best of sampled set (BOSS) algorithm coupled with approximate Bayesian inference. Numerical studies show that the proposed method significantly increases seller revenue compared to classical price experimentation, even for the single-item case. [pdf]