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Some game theoretic marketing attribution models

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  • Elisenda Molina
  • Juan Tejada
  • Tom Weiss

Abstract

In this paper, we propose and analyse two game theoretical models useful to design marketing channels attribution mechanisms based on cooperative TU games and bankruptcy problems, respectively. First, we analyse the Sum Game, a coalitional game introduced by Morales (2016). We extend the ideas introduced in Zhao et al. (2018) and Cano-Berlanga et al. (2017) to the case in which the order and the repetition of channels on the paths to conversion are taken into account. In all studied cases, the Shapley value is proposed as the attribution mechanism. Second, a bankruptcy problem approach is proposed, and a similar analysis is developed relying on the Constrained Equal Loss (CEL) and Proportional (PROP) rules as attribution mechanisms. In particular, it is relevant to note that the class of attribution bankruptcy problems is a proper subclass of bankruptcy problems.

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  • Elisenda Molina & Juan Tejada & Tom Weiss, 2020. "Some game theoretic marketing attribution models," Papers 2012.00812, arXiv.org.
    • Handle: RePEc:arx:papers:2012.00812
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    References listed on IDEAS

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    1. Cano Berlanga, Sebastian & Vilella, Cori, 2017. "Attribution models and the Cooperative Game Theory," Working Papers 2072/290758, Universitat Rovira i Virgili, Department of Economics.
    2. Juan D. Moreno-Ternero, 2007. "Bankruptcy Rules And Coalitional Manipulation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 105-118.
    3. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    4. Kaifeng Zhao & Seyed Hanif Mahboobi & Saeed R. Bagheri, 2018. "Shapley Value Methods for Attribution Modeling in Online Advertising," Papers 1804.05327, arXiv.org.
    5. Hana Choi & Carl F. Mela & Santiago R. Balseiro & Adam Leary, 2020. "Online Display Advertising Markets: A Literature Review and Future Directions," Information Systems Research, INFORMS, vol. 31(2), pages 556-575, June.
    6. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    7. Manuel Pulido & Joaquín Sánchez-Soriano & Natividad Llorca, 2002. "Game Theory Techniques for University Management: An Extended Bankruptcy Model," Annals of Operations Research, Springer, vol. 109(1), pages 129-142, January.
    8. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
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