Netlogo, game theory, and the iterated prisoner’s dilemma

I think it’s safe to say that the Prisoner’s Dilemma is the single most famous illustration of game theory that is out there.

Most of the time, you’re only asked to imagine two rational actors, each deciding whether or not to defect on their partner. But now suppose that you have more than just two actors — suppose, instead, that there is a whole population of people, who constantly meet up and get thrust into the drama of a prisoner’s dilemma.

Further, let’s suppose that these actors have different strategies when they interact. Some folks always cooperate; some always defect. Some will cooperate so long as their partner did last time; others remember being betrayed and hold a grudge. Some are sado-masochists, who will loyally cooperate with those who have punished them sometime in the past; others are cowards, who will only cooperate with those who punished them recently. And some just cooperate or defect randomly. (For fun, you can get a handle on these strategies by imagining they are characters from Batman.)

Using these models, what kinds of strategies do we think will win out in the long run? Do nice guys (“cooperators”) finish last — or does crime really pay? Is it better to forgive, or to be ruthless? Using computer simulations, we can find out! Here are some interesting results from an iterated Prisoner’s Dilemma, simulated using the Netlogo software.*

Equal distribution of strategies
In this scenario (call it ‘the Cosmopolis’), there are an equal number of people using each different strategy. The defectors (who always cheat) come out on top early, and remain ahead throughout. But in the long run, the ‘unforgiving’ punishers eventually outpace the ‘defectors’This is a theme that you see recur in many, many different kinds of scenario.

So that’s interesting. Now what happens if a population — a culture — is dominated by one strategy?

In this case, I’ve overpopulated the culture with cowards, and left a few members of the other strategies kicking around. The result? A case of extreme inequality, where cooperators make very little, while the punishers and defectors make a killing.
Suppose that the culture was dominated by pure selfishness: the majority of people defect as a matter of principle. The result: goods are distributed more or less as it is in the Cosmopolis, except that everybody makes a lot less than they could have otherwise.
By contrast, in a culture of altruists, everybody makes a lot more than they would otherwise. The difference is that the punishers are strangely complacent, never overcoming the defectors. Moreover, the “bad” strategies — defectors, cowards, sado-masochists — come out making the most (which is, in my view, a morally perverse outcome).
Finally, in a culture of punishers, the “good” strategies (the punishers, cooperators, and reciprocators) come out ahead of the “bad” strategies (everybody else). This is a unique feature of this situation, since in most cases cooperation is the least successful strategy.

Going by the iterated Prisoner’s Dilemma, I would argue that the punishment world is, perhaps, the best of all possible worlds. Granted, it isn’t as prosperous as altruism world, but it is a world where you do reasonably well and have an incentive to be good. So perhaps Gene Roddenberry had it right.

* Hat-tip: Daniel Little. Uri Wilensky programmed the initial scenario. I added two new strategies, the ‘coward’ and ‘sado-masochist’.

UPDATE: Some of these results are not replicated by Lasse Lindqvist’s model of the Prisoner’s Dilemma.

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