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