Robert Axelrod Quotes

2. Change the payoffs
A common reaction of someone caught in a Prisoner's Dilemma is that "there ought to be a law against this sort of thing." In fact, getting out of Prisoner's Dilemmas is one of the primary functions of government: to make sure that when individuals do not have private incentives to cooperate, they will be required to do the socially useful thing anyway. Laws are passed to cause people to pay their taxes, not to steal, and to honor contracts with strangers. Each of these activities could be regarded as a giant Prisoner's Dilemma game with many players.

1. Enlarge the shadow of the future
Mutual cooperation can be stable if the future is sufficiently important relative to the present. This is because the players can each use an implicit threat of retaliation against the other's defection-if the interaction will last long enough to make the threat effective. Seeing how this works in a numerical example will allow the formulation of the alternative methods that can enlarge the shadow of the future.

Once again, there is an important contrast between a zero-sum game like chess and a non-zero-sum game like the iterated Prisoner's Dilemma. In chess, it is useful to keep the other player guessing about your intentions. The more the other player is in doubt, the less efficient will be his or her strategy. Keeping one's intentions hidden is useful in a zero-sum setting where any inefficiency in the other player's behavior will be to your benefit. But in a non-zero-sum setting it does not always pay to be so clever. In the iterated Prisoner's Dilemma, you benefit from the other player's cooperation. The trick is to encourage that cooperation. A good way to do it is to make it clear that you will reciprocate. Words can help here, but as everyone knows, actions speak louder than words. That is why the easily understood actions of TIT FOR TAT are so effective.

The tournament results show that in a Prisoner's Dilemma situation it is easy to be too clever. The very sophisticated rules did not do better than the simple ones. In fact, the so-called maximizing rules often did poorly because they got into a rut of mutual defection. A common problem with these rules is that they used complex methods of making inferences about the other player-and these inferences were wrong. Part of the problem was that a trial defection by the other player was often taken to imply that the other player could not be enticed into cooperation. But the heart of the problem was that these maximizing rules did not take into account that their own behavior would lead the other player to change.

The extraordinary success of TIT FOR TAT leads to some simple, but powerful advice: practice reciprocity. After cooperating on the first move, TIT FOR TAT simply reciprocates whatever the other player did on the previous move. This simple rule is amazingly robust. It won the first round of the Computer Tournament for the Prisoner's Dilemma by attaining a higher average score than any other entry submitted by professional game theorists. And when this result was publicized for the contestants in the second round, TIT FOR TAT won again. The victory was obviously a surprise, since anyone could have submitted it to the second round after seeing its success in the first round. But obviously people hoped they could do better-and they were wrong.

Will there be anyone out there to reciprocate one's own initial cooperation? In some circumstances this will be hard to tell in advance. But if there has been enough time for many different strategies to be tried, and for some way of making the more successful strategies become more common, then one can be fairly confident that there will be individuals out there who will reciprocate cooperation. The reason is that even a relatively small cluster of discriminating nice rules can invade a population of meanies, and then thrive on their good scores with each other. And once nice rules get a foothold they can protect themselves from reinvasion by meanies.

So in a non-zero-sum world you do not have to do better than the other player to do well for yourself. This is especially true when you are interacting with many different players. Letting each of them do the same or a little better than you is fine, as long as you tend to do well yourself. There is no point in being envious of the success of the other player, since in an iterated Prisoner's Dilemma of long duration the other's success is virtually a prerequisite of your doing well for yourself.

The advice takes the form of four simple suggestions for how to do well in a durable iterated Prisoner's Dilemma:<p>1. Don't be envious.
2. Don't be the first to defect.
3. Reciprocate both cooperation and defection.
4. Don't be too clever.

In this chapter Darwin's emphasis on individual advantage has been formalized in terms of game theory. This formulation establishes conditions under which cooperation in biological systems based on reciprocity can evolve even without foresight by the participants.

The theory of biological evolution is based on the struggle for life and the survival of the fittest. Yet cooperation is common between members of the same species and even between members of different species. Before about 1960, accounts of the evolutionary process largely dismissed cooperative phenomena as not requiring special attention. This dismissal followed from a misreading of theory that assigned most adaptation to selection at the level of populations or whole species. As a result of such misreading, cooperation was always considered adaptive. Recent reviews of the evolutionary process, however, have shown no sound basis for viewing selection as being based upon benefits to whole groups. Quite the contrary. At the level of a species or a population, the processes of selection are weak. The original individualistic emphasis of Darwin's theory is more valid.

The live-and-let-live system that emerged in the bitter trench warfare of World War I demonstrates that friendship is hardly necessary for cooperation based upon reciprocity to get started. Under suitable circumstances, cooperation can develop even between antagonists.

The cooperative exchanges of mutual restraint actually changed the nature of the interaction. They tended to make the two sides care about each other's welfare. This change can be interpreted in terms of the Prisoner's Dilemma by saying' that the very experience of sustained mutual cooperation altered the payoffs of the players, making mutual cooperation even more valued than it was before.

Just as important as getting cooperation started were the conditions that allowed it to be sustainable. The strategies that could sustain mutual cooperation were the ones which were provocable.

Thus cooperation can emerge even in a world of unconditional defection. The development cannot take place if it is tried only by scattered individuals who have no chance to interact with each other. But cooperation can emerge from small clusters of discriminating individuals, as long as these individuals have even a small proportion of their interactions with each other. Moreover, if nice strategies (those which are never the first to defect) come to be adopted by virtually everyone, then those individuals can afford to be generous in dealing with any others. By doing so well with each other, a population of nice rules can protect themselves against clusters of individuals using any other strategy just as well as they can protect themselves against single individuals. But for a nice strategy to be stable in the collective sense, it must be provocable. So mutual cooperation can emerge in a world of egoists without central control by starting with a cluster of individuals who rely on reciprocity.

Proposition 7. If a nice strategy cannot be invaded by a single individual, it cannot be invaded by any cluster of individuals either.