Robert Axelrod Quotes

Tournament studies, ecological simulation, and theoretical analysis demonstrate: (1) A generous version of tit for tat is a highly effective strategy when the players it meets have not adapted to noise; (2) If the other players have adapted to noise, a contrite version of tit for tat is even more effective at quickly restoring mutual cooperation without the risk of exploitation; (3) Pavlov is not robust.

Proposition 1. If the discount parameter, w, is sufficiently high, there is no best strategy independent of the strategy used by the other player.

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.

Aggregation means the organization of elements of a system into patterns that tend to put highly compatible elements together and less compatible elements apart. Landscape theory predicts how aggregation will lead to alignments among actors (such as nations), whose leaders are myopic in their assessments and incremental in their actions. The predicted configurations are based upon the attempts of actors to minimize their frustration based upon their pairwise propensities to align with some actors and oppose others. These attempts lead to a local minimum in the energy landscape of the entire system. The theory is supported by the results of the alignment of seventeen European nations in the Second World War. The theory has potential for application to coalitions of business firms, political parties in parliaments, social networks, social cleavages in democracies, and organizational structures.

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.

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.

Proposition 3. Any strategy which may be the first to cooperate can be collectively stable only when w is sufficiently large.

The two-person iterated Prisoner’s Dilemma is the E. coli of the social sciences, allowing a very large variety of studies to be undertaken in a common framework.

Proposition 4. For a nice strategy to be collectively stable, it must be provoked by the very first defection of the other player.

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 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.

A moral of the story is that models that aim to explore fundamental processes should be judged by their fruitfulness, not by their accuracy. For this purpose, realistic representation of many details is unnecessary and even counterproductive.

In addition, TIT FOR TAT was known to be a powerful competitor. In a preliminary tournament, TIT FOR TAT scored second place; and in a variant of that preliminary tournament, TIT FOR TAT won first place. All of these facts were known to most of the people designing programs for the Computer Prisoner's Dilemma Tournament, because they were sent copies of a description of the preliminary tournament. Not surprisingly, many of them used the TIT FOR TAT principle and tried to improve upon it. The striking fact is that none of the more complex programs submitted was able to perform as well as the original, simple TIT FOR TAT.

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.

In fact, in the Prisoner's Dilemma, the strategy that works best depends directly on what strategy the other player is using and, in particular, on whether this strategy leaves room for the development of mutual cooperation. This principle is based on the weight of the next move relative to the current move being sufHciently large to make the future important.