Game Theory and Terrorism Risk

The following article, written for Lloyd's by Dr. Gordon Woo, catastrophe research consultant for RMS, was first published in July 2002.

'It is a feature of a democracy that a security service will follow a new security threat than foreseeing it'. This candid declaration appears in the autobiography of Stella Rimington, former director-general of the British Intelligence Service MI5. In 1969, the first year of her career at MI5, she admits there was very little intelligence, and practically no sources of information about the resurgence of the IRA. In 1996, the last year of her career at MI5, Afghan waiters in London were openly soliciting American signatories for flight training in USA. With counter-terrorism intelligence services in western democracies struggling to identify new security threats, how can insurers come to terms with terrorism risk?

Insurers are accustomed to covering earthquake risks, even if some seismic threats remain to be identified.

Just as with natural perils, the objectives of civic authorities and insurers differ in respect of risk assessment. Being responsible primarily for public safety, civic authorities endeavour to warn against specific imminent hazard events. Insurers, on the other hand, seek to quantify the risk not over days, but over a number of months. Suppose that the time and location of a major al-Qaeda attack were decided randomly, such as by the throw of dice. This knowledge would be very instructive for insurers, even though the lack of predictive power on timing would frustrate the deployment of security forces. In fact, it is known that there is a significant random, partly serendipitous, element in an al-Qaeda attack; not without some reason can the outcome be declared an act of God.

From the mathematical perspective of game theory, popularized in the Oscar-winning movie ‘A Beautiful Mind’, the incorporation of a purely chance component into operational decision-making is a virtue: randomizing the choice between alternative strategies helps throw your opponent off balance. If Osama bin Laden tossed a coin in a cave to decide on which of two cities to target, no amount of satellite intelligence would clarify the choice. The larger the random component the bigger the task for the over-stretched security forces. However, for insurers with well-diversified books of terrorism business, this aleatory component in terrorism risk would lend support to the optimistic view that, with a sufficient measure of skill and expertise, this is a class of risk that can be successfully underwritten.

Given the importance of geographical diversification, it is essential for underwriters to track excessive concentrations of urban exposure. Databases of potential commercial, industrial, military, government and diplomatic targets are being assembled allowing underwriters to map their terrorism exposures using geographical information systems.

Even with well separated urban exposures, the prospect of synchronized al-Qaeda attacks across a continent encourages prudence in PML assignments. The launching of synchronized attacks is an al-Qaeda hallmark; one designed to maximize the impact of new modes of terrorism. Recognizing that the level of defence against a new attack mode would inevitably rise after the first such attack, the maximum blow would be struck by aiming for a number of targets at about the same time.

Sensitivity to target hardness is reflected more broadly in the choice of specific al-Qaeda targets. Diligence and patience in target selection greatly improves the likelihood of mission success. With equal purposefulness, the virtues of diligence and patience might usefully be exercised by underwriters in selecting the more secure targets. Security is to terrorism what vulnerability is to earthquakes. If two parts of a building are constructed to different seismic standards, the lower standard construction is more likely to be damaged in an earthquake. Similarly, if two gates to a building have different levels of security protection, the gate with lower security is more likely to be infiltrated by terrorists.

'It is the duty of Muslims to prepare as much force as possible to attack the enemies of God.' Through stark statements such as this, Osama bin Laden gave public notice that, once al-Qaeda had access to weapons of mass destruction, it would not hesitate to use them. With any complex weapon system, there is a cost/effectiveness curve to climb before any attack in earnest can be made with a realistic prospect of success.