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

42 Pages Posted: 10 Jun 2019

See all articles by Raghav Singal

Raghav Singal

Columbia University

Omar Besbes

Columbia Business School - Decision Risk and Operations

Antoine Désir

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Garud Iyengar

affiliation not provided to SSRN

Date Written: May 22, 2019

Abstract

One of the central challenges in online advertising is attribution, namely, assessing the contribution of individual advertiser actions including e-mails, display ads and search ads to eventual conversion. Several heuristics are used for attribution in practice; however, there is no formal justification for them and many of these fail even in simple canonical settings. The main contribution in this work is to develop an axiomatic framework for attribution in online advertising. In particular, we consider a Markovian model for the user journey through the conversion funnel, in which ad actions may have disparate impacts at different stages. We propose a novel attribution metric, that we refer to as counterfactual adjusted Shapley value, which inherits the desirable properties of the traditional Shapley value while overcoming its shortcomings in the context of our application. Furthermore, we establish that this 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 inspired by a real-world large-scale dataset.

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

JEL Classification: C6, C71, M3

Suggested Citation

Singal, Raghav and Besbes, Omar and Désir, Antoine and Goyal, Vineet and Iyengar, Garud, Shapley Meets Uniform: An Axiomatic Framework for Attribution in Online Advertising (May 22, 2019). Available at SSRN: https://ssrn.com/abstract=3392721 or http://dx.doi.org/10.2139/ssrn.3392721

Raghav Singal (Contact Author)

Columbia University ( email )

500 West 120th Street
Mudd 317
New York, NY NY 10027
United States

Omar Besbes

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Antoine Désir

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Garud Iyengar

affiliation not provided to SSRN

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