Technical Note-Dynamic Pricing and Demand Learning with Limited Price Experimentation

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 with 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. Furthermore, we describe an implementation of this pricing policy at Groupon, a large e-commerce marketplace for daily deals. The field study shows significant impact on revenue and bookings.