Cost-per-impression pricing for display advertising

Display advertising has a 39% share of the online advertising market and is its fastest-growing category. In this paper, we consider an online display advertising setting in which a web publisher posts display ads on its website and charges based on the cost-per-impression (CPM) pricing scheme while promising to deliver a certain number of impressions on the ads posted. The publisher faces uncertain demand for advertising slots and uncertain supply of visits from viewers. We formulate the problem as a queueing system, where the advertising slots correspond to service channels with the service rate of each server synchronized with other active servers. We determine the publisher’s optimal price to charge per impression and show that it can increase in the number of impressions made of each ad, which is in contrast to the quantity discount commonly offered in practice. We show that the optimal CPM price may increase in the number of ads rotating among slots. This result is typically not expected because an increase in the number of rotating ads in the system can be interpreted as an increase in the service capacity. However, the capacity increase leads to an increase in the fill rate of the demand (the portion of demand satisfied by the publisher). Hence, the publisher can afford to optimally decrease the arrival rate by increasing the price