The Multiple Attribution Problem in Pay-Per-Conversion Advertising

In recent years the online advertising industry has witnessed a shift from the more traditional pay-per-impression model to the payper-click and more recently to the pay-per-conversion model. Such models require the ad allocation engine to translate the advertiser’s value per click/conversion to value per impression. This is often done through simple models that assume that each impression of the ad stochastically leads to a click/conversion independent of other impressions of the same ad, and therefore any click/conversion can be attributed to the last impression of the ad. However, this assumption is unrealistic, especially in the context of pay-per-conversion advertising, where it is well known in the marketing literature that the consumer often goes through a purchasing funnel before they make a purchase. Decisions to buy are rarely spontaneous, and therefore are not likely to be triggered by just the last ad impression. In this paper, we observe how the current method of attribution leads to inefficiency in the allocation mechanism. We develop a fairly general model to capture how a sequence of impressions can lead to a conversion, and solve the optimal ad allocation problem in this model. We will show that this allocation can be supplemented with a payment scheme to obtain a mechanism that is incentive compatible for the advertiser and fair for the publishers.