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

CentER Discussion Paper Series No. 2016-042

17 Pages Posted: 7 Dec 2016

See all articles by Tjeerd Campen

Tjeerd Campen

Tilburg University - Center for Economic Research (CentER)

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Bart Husslage

Tilburg University - Department of Econometrics & Operations Research

Roy H. A. Lindelauf

Military Operational Science

Date Written: November 21, 2016

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.

Keywords: approximation method; Shapley value; cooperative game theory

JEL Classification: C71

Suggested Citation

Campen, Tjeerd and Hamers, Herbert and Husslage, Bart and Lindelauf, Roy H. A., A New Approximation Method for the Shapley Value Applied to the WTC 9/11 Attack (November 21, 2016). CentER Discussion Paper Series No. 2016-042. Available at SSRN: https://ssrn.com/abstract=2874859 or http://dx.doi.org/10.2139/ssrn.2874859

Tjeerd Campen

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Herbert Hamers (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Bart Husslage

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Roy H. A. Lindelauf

Military Operational Science ( email )

Kasteelplein 10
Breda, 4811 XC
Netherlands

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
53
Abstract Views
301
rank
403,363
PlumX Metrics