Dynamic Pricing with Fairness Constraints

Following the increasing popularity of personalized pricing, there is a growing concern from customers and policy makers regarding fairness considerations. This paper studies the problem of dynamic pricing with unknown demand under two types of fairness constraints: price fairness and demand fairness. For price fairness, the retailer is required to (i) set similar prices for different customer groups (called group fairness) and (ii) ensure that the prices over time for each customer group are relatively stable (called time fairness). We propose an algorithm based on an infrequently-changed upper-confidence-bound (UCB) method, which is proved to yield a near-optimal regret performance. In particular, we show that imposing group fairness does not affect the demand learning problem, in contrast to imposing time fairness. On the flip side, we show that imposing time fairness does not impact the clairvoyant optimal revenue, in contrast to imposing group fairness. For demand fairness, the retailer is required to satisfy that the resulting demand from different customer groups is relatively similar (e.g., the retailer offers a lower price to students to increase their demand to a similar level as non-students). In this case, we design an algorithm adapted from a primal-dual learning framework and prove that our algorithm also achieves a near-optimal performance.