Static Pricing for Multi-unit Prophet Inequalities

Characterizing the Efficiency of Static Pricing Schemes as a Function of the Supply The problem of selling a supply of k units to a stream of customers constitutes one of the cornerstones in revenue management. Static pricing schemes (that output the same price to all customers) are commonly used because of their simplicity and their many desirable properties; they are anonymous, nonadaptive, and order oblivious. Although the efficiency of those schemes should improve as the supply k increases, prior work has only focused either on algorithms that aim for a constant approximation that is independent of k or on the setting where k becomes really large. In contrast, this paper characterizes the efficiency of static pricing schemes as a function of the supply. Our approach stems from identifying a “sweet spot” between selling enough items and obtaining enough utility from customers with high valuations. Subsequent work shows that our pricing scheme is the optimal static pricing for every value of k.