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

52 Pages Posted: 10 Jun 2019 Last revised: 23 Aug 2021

See all articles by Raghav Singal

Raghav Singal

Dartmouth College

Omar Besbes

Columbia Business School - Decision Risk and Operations

Antoine Désir

INSEAD

Vineet Goyal

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

Garud Iyengar

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

Date Written: August 21, 2021

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

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 (August 21, 2021). Available at SSRN: https://ssrn.com/abstract=3392721 or http://dx.doi.org/10.2139/ssrn.3392721

Raghav Singal (Contact Author)

Dartmouth College ( email )

Tuck School of Business
100 Tuck Hall
Hanover, NH 03755
United States

Omar Besbes

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Antoine Désir

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

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

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

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