Tuesday, October 6, 2009

An Eye for an Eye

Game theory has produced many strategies of dealing with competing interests, and through these games we can find new perspective on the difficult issue of Afghanistan.

First we need to define the players. Obviously we, the United States and our western allies are player 1. Player 2, and this is important, is not Afghanistan. We are not at war with the people of Afghanistan, we are trying to help them. No, we are at war with global Muslim extremism, which on 9/11 was based in caves in Afghanistan. So player 2 is Muslim extremism, which is a nebulous concept I know, but they are a nebulous group, united in bombing western nations, so we'll lump them together.

Also important to note is that this is not a one-off game with a single interaction, but rather multiple games played over time. Luckily a bunch of smart guys have used computers to model the possible strategies in a multiple game scenario, and those simulations find the Eye of an Eye strategy, or Tit for Tat, is the most effective:

Tit for Tat
1. Unless provoked, the agent will always cooperate
2. If provoked, the agent will retaliate
3. The agent is quick to forgive
4. The agent must have a good chance of competing against the opponent more than once.

It is the model most people use to get by, and by extension, most countries. There is even a special variant for geopolitics called the Peace War Game, or the "provokable nice guy" strategy. This follows Tit for Tat, with nations cooperating until one side becomes aggressive, triggering retaliation by the other side.. Basically, the player does what his opponent did on the previous move.

According to Tit for Tat, after 9/11 we should have run into Afghanistan (or arguably Saudi Arabia, but that's beyond the scope of this article), made a grand attack that shook the Muslim extremist to their core, and left shortly thereafter (quick forgiveness).

As a man who loves empirical data, I would have been on board with the invasion plan I just laid out based on the strategy's success through history. However, it soon became clear that we are engaged with an enemy unlike any we have faced before.

Muslim extremism is not a country, it is a decentralized network of like minded individuals, sometimes completely independent of the main hierarcy. Many of these people are willing to blow themselves up simply to make a statement. And we respond in turn by sending our soldiers to find other extremists and neutralizing them. Yet they keep coming, despite our best efforts to discourage them.


The advantage of "tit for tat" thus pertains only to a Hobbesian world of rational solutions, not to a world in which humans are inherently social. However, the fact that this solution does not work effectively against groups of agents running tit-for-tat does illustrate the strengths of tit-for-tat when employed in a team (that the team does better overall, and all the agents on the team do well individually, when every agent cooperates).

A one-time, single-bit error in either player's interpretation of events can lead to an unending "death spiral". In this symmetric situation, each side perceives itself as preferring to cooperate, if only the other side would. But each is forced by the strategy into repeatedly punishing an opponent who continues to attack despite being punished in every game cycle. Both sides come to think of themselves as innocent and acting in self-defense, and their opponent as either evil or too stupid to learn to cooperate.

As evidenced by their respective simulations, Tit for tat and the Peace War game are ideal when dealing with organized teams of (mostly) rational actors. It is clear that this is not the situation we are engaged in, as our enemy is highly decentralized (thus disorganized) and fairly irrational (suicide bombers). Also, the extremist movement considers our very existence a punishable offense. Tit for tat will fail to give us the ideal outcome.

Therefore our military leadership appears to have put us on a different strategy, the Grim trigger (Tit for tat is also a trigger strategy).

As the name suggests, the Grim trigger game is no fun. A nation involved in the Grim trigger strategy responds to aggression with indefinite retaliation. This is costly and less effective than a Tit for tat strategy, but we are left with few options. That being said, we cannot realistically continue this war forever, so now we move into the realm of deterrence.

Deterrence, or more specifically Massive retaliation, is the use of overwhelming force in reponse to aggression, and thereby discouraging future aggression. In a way, we're back to Tit for tat, except this time a huge Tit for each tat.

We even have the forgiveness component, as we have shifted gears from rooting out Al Qaeda and the Taliban to civilian protection mode.

"Tit for Tat with forgiveness" is sometimes superior. When the opponent defects, the player will occasionally cooperate on the next move anyway. This allows for recovery from getting trapped in a cycle of defections. The exact probability that a player will respond with cooperation depends on the line-up of opponents.

Mixed with intelligence gathering and law enforcement to catch the highly irrational actors, we have a comprehensive strategy to fight this ideological aggression. It's not perfect, and it won't work 100%, but considering the circumstances it is our best bet. Plus, we have the possible added bonus of Afghanistan becoming a free market democracy.

Regardless, if stopping terrorist attacks is our main goal, which it is, we really don't have any other options.

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