Shapley Meets Uniform: An Axiomatic Framework for Attribution in Online Advertising

Abstract

One of the central challenges in online advertising is attribution, namely, assessing the contribution of individual advertiser actions such as e-mails, display ads and search ads to eventual conversion. Several heuristics are used for attribution in practice; however, most do not have any formal justification. The main contribution in this work is to propose an axiomatic framework for attribution in online advertising. We show that the most common heuristics can be cast under the framework and illustrate how these may fail. We propose a novel attribution metric, that we refer to as counterfactual adjusted Shapley value (CASV), which inherits the desirable properties of the traditional Shapley value while overcoming its shortcomings in the online advertising context. We also propose a Markovian model for the user journey through the conversion funnel, in which ad actions may have disparate impacts at different stages. We use the Markovian model to compare our metric with commonly used metrics. Furthermore, under the Markovian model, we establish that the CASV metric coincides with an adjusted "unique-uniform" attribution scheme. This scheme is efficiently implementable, and can be interpreted as a correction to the commonly used uniform attribution scheme. We supplement our theoretical developments with numerical experiments using a real-world large-scale dataset.

Keywords: digital economy, online advertising, attribution, Markov chain, Shapley value, causality

JEL Classification: C6, C71, M3