C O O P E R A T I O N   4

How Cooperation Works

What actual, emotion-driven human beings do with individual choices of cooperation or defection is, of course, unpredictable. But in general, rational players will tend to make similar choices. This allows those interested in human behavior to work out some mathematical predictions of behavior that, interestingly, can be shown to be always true.

In this case, it turns out that a careful choice of the four payoffs for cooperation or defection results in being able to say that there exists a rational choice of cooperation, even in the midst of a majority of defectors. Specifically, Axelrod found that if just four conditions were met, cooperation can be the most rational choice--even in a population consisting almost entirely of defectors.

First, the players must be able to recognize one another. Anonymity, becauses it decreases the penalty for defection in an environment of iterated interactions, tends to work against the evolution of a population of cooperators.

Second, the total number of potential opportunities for interaction must be unknown to each player. It is the uncertainty preventing players from calculating just how much defection they can get away with that decreases the long-term reward for defection. If you don't know when your final interaction will be, and thus can't plan to defect on that turn, you must take into your calculations the fact that what you do on this interaction will affect the response to you on the next interaction. This creates an incentive to cooperate.

Third, the payoff for mutual cooperation (that is, both players cooperate with each other) in each interaction must be greater than the average payoff of a cooperation-defection (the payoff to the defector plus the sucker's payoff divided by 2). In mathematical terms, this is the condition in which R > (P + S) / 2.

Fourth and last, there must be a certain minimum proportion of cooperating players in the population... and here was one of the greatest surprises. Axelrod calculated that--amazingly--if all the preceding conditions are met, and there is a high probability that players which have interacted before will do so again (specifically, ninety percent), then cooperation can eventually evolve to include the entire population if only five percent of the total initial population consists of cooperators. It's reasonable to expect that there must be enough cooperators so that they can create a sort of island of trust in a sea of defection. What's surprising is that so few are necessary.

Next:

How Tit for Tat Works

How Cooperation Works

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