Dynamic Pricing and Demand Learning with Limited Price Experimentation

Abstract

In a dynamic pricing problem where the demand function is not known a priori, price experimentation can be used as a demand learning tool. Existing literature usually assumes no constraint on price changes, but in practice sellers often face business constraints that prevent them from conducting extensive experimentation. We consider a dynamic pricing model where the demand function is unknown but belongs to a known finite set. The seller is allowed to make at most m price changes during T periods. The objective is to minimize the worst case regret, i.e., the expected total revenue loss compared to a clairvoyant who knows the demand distribution in advance. We demonstrate a pricing policy that incurs a regret of O(log^(m) T), or m iterations of the logarithm. We further show that this regret is the smallest possible up to a constant factor. Our analysis provides important structural insights into optimal pricing strategies. Finally, we describe an implementation at Groupon, a large e-commerce marketplace for daily deals. The field study shows significant impact on revenue and bookings.