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...