Market Curiosity: Exploring Markets And Systems

March 6, 2011

Scientific basis for the evolution of cooperation

Filed under: Favorite Posts, Systems — Tags: , , — Jeff Fitzmyers @ 2:02 pm

Another investigation which has strongly influenced the artificial life community is Robert Axelrod’s game theoretic simulation of the evolution of cooperation. By letting different strategies compete in a repeated Prisoner’s Dilemma game, Axelrod (1984) showed that mutually cooperating, “tit-for-tat”-like strategies tend to dominate purely selfish ones in the long run….

Reciprocal Altruism
The “prisoner’s dilemma” may be overcome by a strategy of “tit-for-tat”, which reciprocates to cooperation by cooperation and to defection by defection. This makes it impossible for selfish individuals, who defect, to gain long-term advantages from reciprocal cooperators, since these will only cooperate with those that cooperate themselves. Yet two “tit-for-tat” players will spontaneously start to cooperate thus reaping the benefits of continuing synergy (Axelrod, 1984).

Critique: at the first encounter, none of the players knows how the other one will respond. In order to have a chance to start a cooperative exchange the reciprocal altruist must start with a cooperative move, which can be taken advantage of by a defector…

Can’t avoid exposure to not nice people.

The strategy only starts to pay when there are repeated encounters with the same individual, so that the gains of continuing cooperation outweigh the losses of first-time encounters with defectors. It also implies that players should recognize different partners and remember their last moves toward a given partner in order to choose the appropriate next move. This is insufficient to explain a complex ultrasocial system, where many encounters are first-time.

Thus the need for “reputation”.

This scheme is very simple to learn: use “cooperate” as a default initial condition, and further just mimic the behavior of the partner. If the partner uses the same scheme (or an even more altruistic one) a mutually beneficial cooperative relation will develop. If the partner defects, the exchange will stop before much harm is done. Such a cognitive strategy will therefore in general be beneficial to the partners, and thus be repeated. This means that others, observing the beneficial behavioral pattern, will tend to imitate it, taking over the cognitive scheme. That by definition makes a meme.

The strategy only pays off if one can distinguish partners and remember whether they cooperated or defected during the last encounter. Otherwise, every encounter is like a one-shot prisoner’s dilemma, in which it pays to defect. In small groups, where interactions tend to be repeated often, a pure tit-for-tat strategy might flourish, as there would be little demands on memory. In larger groups, however, where many encounters happen for the first time, or are repeated only after a long interval in which the memory of the previous encounter might have faded, a different rule would be needed to avoid invasion by defectors.

A rule is not needed when persistent, transparent, and verifiable “memory” is available: reputation. Which then negates the usefulness of punishment:

As memes tend towards homogeneity within communicating groups (and towards heterogeneity between non-communicating groups), we might expect that after a while most members of a group G would follow the same general “tit-for-tat-like” strategy. It would then be more efficient not to distinguish between different individuals X1 or X2 in the group, but use the general rule of ingroup altruism:

– If X belongs to group G, then cooperate
– If X does not belong to group G, then defect, since encounters with other groups will tend to be one-shot, it would pay to defect, and thus we could expect a complementary rule of outgroup hostility to evolve as a generalization of “defect from defectors”:
– If X belongs to group G and X defects, then punish X. Finally, the retaliation inherent in the original “tit-for-tat” strategy, as a means of protection against invading cheaters.
– What is considered “defection” will evolve to encompass gradually more diverse and complex patterns of behavior (e.g. lying, stealing, cheating, tresspassing rules, murdering, adultery, incest, etc.).

Update December 26: Also, punishment is superseded by shunning.

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