The secret ingredient to solving social dilemmas is punishment. Without the ability to punish transgressors, good behavior must rely entirely on individual self-control in abstaining from the temptation to cheat and obtain a reward. Some individuals are up to this challenge. Their consciences are so strongly developed to chasten them for engaging in dishonorable behavior that this is not a problem. But for most, it is. Indeed, a fundamental human weakness is to go for today's reward over tomorrow's, a failing which destroys most attempts at dieting let along social dilemmas.
Sufficient punishment fixes this problem by adding the force of extrinsic incentives to intrinsic. Given sufficient reinforcement, even those more "pragmatic" consciences can be persuaded to do the right thing. Yet, even when such punishments are available, a literal-minded view of game theory suggests that they must always be available. Individuals must never perceive themselves as getting off scot free. The usual version of this argument uses look forward, reason back type reasoning. Suppose the game will end in period N. Then clearly bad behavior in that period is unpunishable and hence everyone will be bad. But this destroys punishment for bad behavior in the penultimate period, and so on. The pure logic of the situation implies that any game known to end at a fixed time, however far into the future, will see cooperation remorselessly break down right from the start.
But, while logically sound, this is a very silly prediction when the number of periods is long. Despite the logic of LFRB, bad behavior in early periods will be punished and good behavior rewarded with reciprocity in early periods of the game, only breaking down when the endgame is sufficiently close. Here again we see the friendly face of irrationality. Suppose there is some chance that others playing the game don't "get it." They, instead, think they are playing the infinitely repeated version of the game whereby cooperation can be sustained by threats of punishment, and play accordingly.
What is a rational soul to do? The answer is, when in Rome, do as Romans do. In other words, pretending that you too don't get the game is a perfectly logical and sensible response, at least until some point deep in the game where knowledge that punishment won't work becomes too hard to ignore. As with some of our other examples, only a seed of doubt about the rationality of others is needed so long as the endgame is sufficiently far off into the future. Such a seed of doubt seems to me eminently more reasonable than the maintained assumption in the standard model, that everyone understands the game perfectly,
But if we're playing a short game consisting of, say, only 8 periods. Now the logic of LFRB has real force, and we would seem to be genuinely doomed. Running such a game in the lab reveals that things are not quite as bad as all that, but they are definitely pretty bad.
Or maybe not. Let's change the game a little. Suppose, at the end of each period, each player has a chance to punish one or more of the others. Punishment involves destroying some of their payoffs. But this punishment is not free, it costs the punishing individual something as well. This would seem of immense help since the whole problem was that we lacked an ability to punish in the last period and, this wrecked the incentives in all the earlier periods. Now, we no longer have this problem. If someone misbehaves in the last period, we punish them via value destruction and all is once again well in the world. But such a plan only works if the punishment is credible, if we can count on the punishment to be delivered should an individual try to test societal resolve. There are two problems with credibility. First, there is a social dilemma in who delivers the punishment. While we all might agree that cheaters should be punished, each of us would rather that someone else delivers the punishment and hence takes the hit to their own payoffs. But even if we sorted this out by agreeing on whose job it was to punish, we might still be in trouble. In the last period of the game, who would actually carry through with the punishment?
This is a version of our earlier problem. In the last period, there is no future reward for today's good behavior nor punishment for bad. Since the whole point of punishing is to obtain future good behavior, what is the point of punishing anyone in the last period of the game? Worse yet, not only is punishment pointless, but it is also costly. So why would anyone believe that misbehavior will be punished in the last period? By the same logic, there is no point in punishing in the penultimate period either and again the endgame casts its long shadow back to the first period. Irrationality seems to work less well as a way out of this particular logical bind. The endgame is simply too near.
Yet, remarkably, such schemes seem to work, at least in western cultures. Economists Ernst Fehr, Simon Gaechter, and a number of other co-authors performed versions of this experiment in labs in the US and Europe. Remarkably, they found the such a scheme proved excellent at producing cooperation. Some individuals tested societal resolve early in the game and invariably received bloody noses for this insolence.
But why does it work? The answer, in this case, seems to be morality. While conscience is weak in resisting temptation, it is rather stronger when we have a chance to unsheathe the sword of justice to be used on others. That is, even though there was a personal cost to punishment, it seemed to be more than offset by a personal benefit in administering justice.
[A curious sidenote to this stories, in Middle Eastern, Greek, and North African cultures, the sword of justice operated in the other direction---those who did not cheat were punished. That is, individuals cooperating in a prisoners dilemma were hit with penalties from those who did. This soon produced conformity in a failure to solve social dilemmas.]
This solution is all well and good when the punishment can be surgically directed at transgressors, but suppose instead that there is collateral damage--to punish the guilty, some innocents must be punished as well. In work in progress by myself and former Berkeley undergrad Seung-Keun Martinez, we investigate this possibility. We first consider the opposite extreme where, to punish one person, you must punish everyone. One might think that such a scheme would be either marginally useful or utterly useless. In fact, it is neither. Compared to the world in which no punishment was allowed, punishment of this sort actually reduces cooperation. This is not simply from the value destroyed by punishment (though there is some of that), but rather from a reaction to the possibility of such punishment. When individuals fear suffering punishment when doing the "right thing," they seem to become despondent and to cooperate less than those under no such threat.
We are now in the process of investigating intermediate levels of "collateral damage" from punishment to determine where the 'tipping point" might lie.