Learning While Pricing Fairly: Queue-Regularized Exploration for Pricing Experiments

Pricing experiments generate information about demand, but the prices used for learning are also the offers that different customer groups receive. We study how a seller can reduce differences between group-average prices while retaining the random variation needed for demand estimation. We extend Random Shock Design (RSD) with a fairness penalty scaled by virtual queues. This fairness-regularized RSD (FRSD) uses past disparities to correct the next price, then adds an independent shock for demand estimation. Under bounded demand and a well-conditioned regression design, we bound terminal price disparity and establish vanishing disparity at zero tolerance with diminishing shocks, while demand estimation remains consistent. The revenue analysis separates learning error from price adjustments; a fair benchmark and separate lower bounds identify the cost of terminal fairness. Experiments compare FRSD with RSD, fixed penalties, and current-gap penalties. Synthetic results include a 92% reduction in mean disparity alongside a 2.4% increase in mean revenue relative to RSD with the same estimation and exploration settings. In the Online Retail-calibrated simulation, FRSD reduces disparity by 19% with small costs in revenue and estimation accuracy.