Game Theory, Prisoner’s Dilemma, Nash Equilibrium, Stag Hunts, and Sherlock Holmes…and Counter-Terrorism? 2/2
So, you’ve read my previous post about Game Theory, and you want to know more. No problem, there is plenty more to cover.
Application to Counter-Terrorism Policy
Three seperate assumptions highlight preemption vs. defense when referring to Counter-Terrorism. Each one looks at different parts of a chart like the one we saw with the Prisoner’s Dilemma. In this example, a country, the United States, can preempt terrorists, or they can defend against them, or do nothing. Country two, Canada, has the same options. Let’s look at the first set of assumptions with respect to preemption.
Canada
|
United States (down) |
Preempt |
Inaction |
Defend |
|
Preempt |
4,4 |
-2,6 |
-8,8 |
|
Inaction |
6,-2 |
0,0 |
-6,2 |
|
Defend |
8,-8 |
2,-6 |
-4,-4 |
So, the first set of assumptions say that the US and Canada are equally targetted by the same terrorist group, the countries can preempt, do nothing, or defend, and assume that it costs 8 points to preempt, and the return on that expenditure is 6 points. Look at the (Red) numbers. The US preempts and gets a -2 (6 – 8 = -2) and Canada does nothing and gets a 6 (6+0). What do you see in those four highlighted boxes? A Prisoner’s Dilemma where rational, self-interested actions result in overall unsatisfactory outcome. Each country can free-ride (do nothing) and be the best off. In this case, inaction is the dominant strategy for each country. This leads to a zero-zero outcome, which is a Nash Equilibrium because neither country has incentive to preempt, regardless of what the other country does.
Now we look at the same chart with respect to defending.
Canada
|
United States (down) |
Preempt |
Inaction |
Defend |
|
Preempt |
4,4 |
-2,6 |
-8,8 |
|
Inaction |
6,-2 |
0,0 |
-6,2 |
|
Defend |
8,-8 |
2,-6 |
-4,-4 |
In this case, we are assuming again that both countries are equally targeted by the same terrorist group, and can preempt, do nothing, or defend. But now, we also assume that Defending costs 6 points, and returns 8 to the defending country alone. But, the defenders efforts make the other country more vulnerable and costs them 6. Inaction returns the best overall return, if they both defend, they each spend 6, get 8 back, but are cost another 6 by the other country’s defense (8-6-6=-4). What we have here is a second prisoner’s dilemma. The Nash Equilibrium here is mutual defense, because it is the best unilateral course of action regardless of what the player does.
Take in a deep breath, one more to go. Now, we hold the assumptions of being equally targeted and actions the same, and add that cost of preemption and defense also do not change. Now, we can compare preemption to defense on the same chart.
Canada
|
United States (down) |
Preempt |
Inaction |
Defend |
|
Preempt |
4,4 |
-2,6 |
-8,8 |
|
Inaction |
6,-2 |
0,0 |
-6,2 |
|
Defend |
8,-8 |
2,-6 |
-4,-4 |
We see the third and final prisoner’s dilemma. The Nash Equilibrium is again mutual defense, because the other two options have one country losing 8.
Game Theory influences allocation of resources between defense and preemption in the Counter-Terrorism world. It also shows how terrorists exploit asymmetric relationships to probe for weakest links and leads to rational actor-based policies such as the no negotiation policies in the US and Israel. It is, however, limited in that it assumes the countries will always maximize their outcomes. It says that countries will always act rationally, which is often defined in terms of the observer’s own cultural/societal framework. Also, not all the payoffs can be quantified and some real-world payoffs do not follow the theory, such as the post-911 US.
Source: Sandler & Enders, “Applying Analytical Methods to Study Terrorism,” International Studies Perspectives (2007) 8, 287-302
If you have any questions or comments on this, please comment, or email me with your thoughts!
