October 04, 2006

DON'T HATE THE GAME (THEORY) 3: AND THE WINNER IS...


Caption: These two cooperate pretty well most days.

This is the third post in a series about how cooperation can develop in world motivated largely by self-interest. The applications from game theory can be very useful in getting things done in all kinds of settings.

If this is your first visit, please scroll down to the two earlier entries. The first introduced the topic and the second explained the Prisoner's Dilemma, a scenario often used to study situations where two parties can chose to cooperate or defect.

The best strategy here depends on whether this is a one-time game (or a game with a fixed number of rounds) or whether players will meet an indefinite number of times. In a one-time meeting, the temptation to defect is so high and the punishment for being a sucker is so severe that there is no incentive to cooperate. The least risky strategy is to defect.

(Translation: one-time interactions don't bring out the best in people. This is one more reason why it might not be a good idea to buy a new computer or a magic whistle from a total stranger who just appeared on the sidewalk.)

However, the incentives change if there are an indefinite number of interactions, as is often the case in real life. This situation is called the iterated Prisoner's Dilemma. Despite the risks, both parties can gain more by cooperating than defecting.

In The Evolution of Cooperation, Robert Axelrod describes computer tournaments held to test strategies in an iterated Prisoner's Dilemma scenario. Surprisingly, the best overall performer was also the shortest and simplest, TIT FOR TAT, which starts out by cooperating and then does whatever the other player did on the previous move.

TIT FOR TAT has the following advantages: it is nice, provocable, forgiving, and clear. Specifically,

*It's nice because it is never the first to defect (strategies that defect first are mean). Two players both using TIT FOR TAT can both do very well. In fact, "TIT FOR TAT succeeds without doing better than anyone with whom it interacts. It succeeds by eliciting cooperation from others, not by defeating them."

*It's provocable because it retaliates when the other party defects. This makes the consequences of defection unpleasant and encourages cooperation.

*It's forgiving because it resumes cooperation as soon as the other party does.

*It's clear because the other player doesn't have to be a rocket scientist to figure it out. In fact, a player using TIT FOR TAT has little to lose by proclaiming the strategy in advance.

Computer modeling shows that communities using TIT FOR TAT can withstand invasion by mean strategies and that a small number of cooperators entering a larger population of meanies can still do pretty well. There are also examples from nature and history of TIT FOR TAT-like strategies achieving cooperation without friendship or understanding.

Next time: practical applications (there are lots).

GOAT ROPE ADVISORY LEVEL: ELEVATED

1 comment:

Jeff Allen said...

I think that this is why the Church can be effective in social change - it has long-term relationships with other institutions. Dietrich Bonhoeffer's observation on Church-state relations is also helpful:

"In the first place (the church) can ask the state whether its actions are legitimate and in accordance with its character as state, i.e., it can throw the state back on its responsibilities. Secondly, it can aid the victims of state action. The church has an unconditional obligation to the victims of any ordering of society, even if they do not belong to the Christian community (!). The third possibility is not just to bandage the victims under the wheel, but to put a spoke in the wheel itself."

Peace,

Jeff Allen