A New Approximation Method for the Shapley Value Applied to the WTC 9/11 Terrorist Attack

Herbert Hamers, Bart Husslage, R. Lindelauf, Tjeerd Campen

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Abstract

The Shapley value (Shapley (1953)) is one of the most prominent one-point solution concepts in cooperative game theory that divides revenues (or cost, power) that can be obtained by cooperation of players in the game. The Shapley value is mathematically characterized by properties that have appealing real-world interpretations and hence its use in practical settings is easily justified.
The down part is that its computational complexity increases exponentially with the number of players in the game. Therefore, in practical problems that consist of more that 25 players the calculation of the Shapley value is usually too time expensive. Among others the Shapley value is applied in the analysis of terrorist networks (cf. Lindelauf et al. (2013)) which generally extend beyond the size of 25 players. In this paper we therefore present a new method to approximate the Shapley value by refining the random sampling method introduced by Castro et al. (2009). We show that our method outperforms the random sampling method, reducing the average error in the Shapley value approximation by almost 30%. Moreover, our new method enables us to analyze the extended WTC 9/11 network of Krebs (2002) that consists of 69 members. This in contrast to the restricted WTC 9/11 network considered in Lindelauf et al. (2013), that only considered the operational cells consisting of the 19 hijackers that conducted the
attack.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages17
Volume2016-042
Publication statusPublished - 21 Nov 2016

Publication series

NameCentER Discussion Paper
Volume2016-042

Keywords

  • approximation method
  • Shapley value
  • cooperattive game theory

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    Hamers, H., Husslage, B., Lindelauf, R., & Campen, T. (2016). A New Approximation Method for the Shapley Value Applied to the WTC 9/11 Terrorist Attack. (CentER Discussion Paper; Vol. 2016-042). CentER, Center for Economic Research.