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 emails, 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, which 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 data set. This paper was accepted by David Simchi-Levi, revenue management and market analytics.

Optimizing Audio Recommendations for the Long-Term: A Reinforcement Learning Perspective

“…The next lemma shows that, in expectation, the cumulative sum of credited values equals the true difference in long-term value, up to a second order term. This property is similar to what Singal et al [2022] call counterfactual efficiency in their axiomatic approach to coherent attribution. The term that is O(β 2 ) depends on the degree of distribution shift and is described explicitly in Appendix C.4.…”

A Graphical Point Process Framework for Understanding Removal Effects in Multi-Touch Attribution

“…These rule-based heuristics can still be easily employed for the path-topurchase data, but they either ignore the effects of other touchpoints or do not consider the interactive effects among touchpoints. They are also criticized for being biased and lacking rationale justifying their appropriateness as attribution measures (Singal et al 2022).…”

“…The main novelty of previous work in this category comes from the following two perspectives. The majority of research focuses on proposing new models to describe user behavior (e.g., Shao & Li 2011, Breuer et al 2011, Danaher & van Heerde 2018, Xu et al 2014, Zhao et al 2019, while the others focus on studying the attribution scoring methods such as the justification and fairness of Sharpley value (e.g., Dalessandro et al 2012, Singal et al 2022).…”

“…However, it is important to account for the exciting effects of these touchpoints. Also, as pointed out by Singal et al (2022), there exists little (if any) theoretical justification for the attribution based on the incremental value.…”

“…Due to the nature of the Shapley value, it typically provides channel-level but not path-level attribution or touchpoint-wise attribution scores. In addition, existing methods based on Shapley value did not take into account the temporal distance between touchpoints in the path-to-purchase data, including (Dalessandro et al 2012, De Haan et al 2016, Kireyev et al 2016, Berman 2018, Singal et al 2022. For example, the most recent work by Singal et al (2022) used a discrete Markov chain model to describe the transitions in a customer's state along the customer journey through the conversion funnel, which does not incorporate the temporal distance when the customer moves from a state to another state in one transition.…”