Targeting by Transnational Terrorist Groups

Abstract

Many successful terrorist groups operate across international borders where different countries host different stages of terrorist operations. Often the recruits for the group come from one country or countries, while the targets of the operations are in another. Stopping such attacks is difficult because intervention in any region or route might merely shift the terrorists elsewhere. Here, we propose a model of transnational terrorism based on the theory of activity networks. The model represents attacks on different countries as paths in a network. The group is assumed to prefer paths of lowest cost (or risk) and maximal yield from attacks. The parameters of the model are computed for the Islamist–Salafi terrorist movement based on open source data and then used for estimation of risks of future attacks. The central finding is that the United States (US) has an enduring appeal as a target, due to lack of other nations of matching geopolitical weight or openness. It is also shown that countries in Africa and Asia that have been overlooked as terrorist bases may become highly significant threats in the future. The model quantifies the dilemmas facing countries in the effort to cut terror networks, and points to a limitation of deterrence against transnational terrorists.

Appendix

1.1 1 Global Sensitivity Analysis

Considerable uncertainty exists above the values of the model parameters: the supply of plots, translocation costs, interception costs and the yields. Indeed, is likely that the estimates of those parameters in Sect.3 are different from the ones used by the terrorist groups. To explore the sensitivity of the predictions to this uncertainty we considered 100 realizations of the model, each with different parameter values. In each realization, each of the original values of the parameters was randomly changed: the value was multiplied by a random number sampled uniformly from [0.5, 1.5]. Thus, the values were varied through a range of ± 50%.

Table 4 shows the sensitivity in the expected number of attacks against various countries. In the majority of cases, the expected number of attacks changes by ± 10%, often less. The reason for this is that paths in the networks become sums of random quantities, and errors tend to partially cancel each other when summed (central limit theorem). The highest sensitivity was observed in the attacks against the US in the scenario when the US is protected against foreign plots. In such a case, the number of attacks in the US varies exactly as the number of plots that start in the US.

Table 4 Expected number of plots and sensitivity to parameter estimates

The values of λ (the determinism in the path selection, explained in Appendix 2) was kept at its default value (0.1) since λ directly expresses sensitivity. In the limit of $\lambda\to0$, the terrorist groups is completely insensitive to risk or cost while in the limit $\lambda\to\infty$ the sensitivity is infinite and even small changes in costs can lead to arbitrarily large changes in path choice. The regime $\lambda\to\infty$ is the case where a decision maker can distinguish arbitrarily small differences in utility and never makes mistakes. Fortunately, clandestine and illicit decision makers like terrorist leaders are far from this omniscient regime.

1.2 2 Computation of Probabilities

In the framework of the theory of complex networks, attack plots could be represented as the motion of an adversary through a weighted network (the plot itself is the adversary we wish to stop). The adversary aims to find an attack path or to hide, whichever plan has the lowest cost. To map such a decision to the framework of activity networks, connect the “attack” and “abandon” nodes in Fig. 2 to a node termed “end” with edges of cost 0. Thus, an attack on a country j corresponds to an adversary that starts at country i and goes through country j and then to the node “attack” and finally to “end”. The decision to abandon corresponds to an adversary that starts at country i then goes to “abandon” and then to “end”. The expected number of attacks on a particular target t can be computed by combining information about path costs with information about the supply of plots from a particular country S _i and the yield of abandonment A. Namely, it is the number of trips from all sources that arrive to the “attack” node from target country t.

The least-cost path corresponds to the optimal choice by the terrorists, but they can make mistakes. An attack plan under uncertainty could be described as a Markov chain [20]. The chain has initial distribution proportional to S _i , and a transition probability matrix M describing the likelihood of taking a particular edge on the network. The “end” node is the absorbing state of the chain. The M matrix can be computed using the least-cost guided evader model described in [20]. Briefly, for each edge (u, v) of the network, the transition probability through it is given by the formula

$$M_{uv}=\frac{\exp\left[-\lambda\left(c(p_{uv})-c(p_{u*})\right)\right]}{\sum_{w}\exp\left[-\lambda\left(c(p_{uw})-c(p_{u*})\right)\right]}\,, $$

where $c(p_{u*})$ is the cost of the least-cost path from node u to the end node, and $c(p_{uv})$ is the cost of the path through edge (u, v): $p_{uv}=(u, v)\cup p_{v*}$. The sum in the denominator runs over the neighbors of node u. Thus, the model generalizes the least-cost path model³. The parameter λ was set to 0.1, in the reported data, but its value has a smooth effect on the predictions of the model because of the smoothness of the exponential function. The number of plots against a target country t is now found by taking the probability of a trip to that target multiplied by the total number of plots ($=\sum_{i}S_{i}$).