Terrorism And Game Theory

Terrorism is a rare, broad concept that affects individuals, schools, corporations, and governments alike. Generally terrorists end up wanting to make change with governments, and governments are usually the only groups powerful enough to try to deal with governments. But what should be the best strategy to deal with terrorists? Since September 11, 2001 game theory has been used to analyze how governments and how terrorists should act to achieve their best outcome. This paper will analyze the games that these competing forces can use to determine the best course of action.

The current war on terrorism is tending to have three different sides: the United States, the European Union, and the terrorists. Before the September 11th attacks all policies towards terrorism were reactive rather than proactive. So before we get involved with terrorists at all, there is a game in which based on what policy the EU is going to enact, the how should the US act towards terrorism. A proactive policy means that the government is going to attack POSSIBLE terror threats, whereas a reactive policy would mean that there would be no strikes against terrorism unless the terrorists decide to strike first.

Now lets take a look at a model. Lets say, for analysis sake, that a proactive strategy costs a government 6, but casts a benefit of 4 for both governments. For example, if only the US has a proactive strategy, then it's net would be -2, but the EU would get all 4 of benefit. If both governments are proactive, then the cost is still 6 for each, but the benefit is doubled to 8 because they benefit from each other's policies. Using this structure, we can construct this normal form of the game:

from Acre & Sandler Vol. 34

In this model it is clear that the Nash Equilibrium is where neither government has a proactive policy towards terrorists. Because neither government is willing to bear the entire cost, neither government will be proactive although the largest benefit can be derived from both being proactive. This is why this is a type of prisoner's dilemma game.

Real life is hardly ever as fair as this model would suggest. The United States is the target of 40% of all terrorism in the world. (Oster) The US is also more often successful in thwarting terrorism than Europe. Thus, a more realistic model might be one in which the United States gets a benefit of 8 for it's proactive strategy. The EU still retains its ability to freeload for a benefit of 4 if they remain reactive while the US is proactive. This more realistic model would be represented in this manner:

from Acre & Sandler Vol. 34

In this model, because the US is always better off if it has a proactive policy, thus giving it a dominant strategy of being preemptive. Because the US has a dominant strategy, the Nash equilibrium is moved up to wherever the EU can maximize benefit given the US being proactive. This is quite possibly the case after the aforementioned September 11th attacks, because although the US policy was immediately reactive, now they are more proactive, while Europe tends to enjoy the benefits presented by the United States.

Before we analyze which of these situations is most likely to occur in the real world, let's take a slightly different look at the situation. Let's assume that there is now a coordination game that the governments