02 July 2009

The Iterated Prisoner's Dilemma: A meta-solution for evolution

Dennett's example of the prisoner's dilemma, used as a backdrop for the evolutionary stable strategy (ESS) of Maynard Smith, may be a foundational explanation for adaptation. Adaptation is best illustrated in Frankl's Man's Search for Meaning: “Life ultimately means taking the responsibility to find the right answer to its problems and to fulfill the tasks which it constantly sets for each individual. (p98)” Adaptation is a characteristic of an organism that has been favored by natural selection. In a sense, if an organism has two evolutionary “choices”, a long neck or a short one, the one that provides to best chance for continued existence of the organism is the most likely one to be selected. Negative characteristics, mutants, may remain for a few generations, but the effect on the organism is generally extinction (organism or characteristic). A cornerstone of Darwinian evolution is the drive for replication, continued existence. Dennett fervently supports adaptation as being necessary to continued existence, that it is an optimality assumption.

Dennett relies on Dresher and Flood's prisoner's dilemma to explain Maynard Smith's evolutionary stable strategy (ESS), a theory in evolutionary game theory. The prisoner's dilemma is quite simple in its design. Two people are each given two choices, to either cooperate (stay quiet) or to defect (implicate the other), with established payoffs. This builds a payoff in a 2x2 matrix. If both defect the payoff is zero, both cooperate the payoff is 2, and if one defects and the other cooperates, the payoff is -1 and 4, respectively. Dennett slightly changes the payoffs (reverses the choices) in order to make his point. This may actually corrupt the game, as it weights the optimal choice to be cooperation. But even so, an ESS can be established, with both players selecting what is optimal for themselves, continual defection in the classic game and in Dennett's version.

The question arises then: if mutual cooperation is beneficial (Dennett's version) and since genetical (physical stance) there is bounded rationality (near-optimal behavior in regards to goals, or “as-if” rationality), which in turn should theoretically mean that at the gene level of an organism mutual cooperation would be the standard, with defection as an aberration. But Dennett takes the stance that the suboptimal always defect, which is not the same as near-optimal, is the standard. While adaptation is still a viable theory, ESS comes into question. Paraphrasing Dawkins, ESS is a strategy that competes well with like organisms (clones?), and is a strategy of domination (p254). ESS by definition is a stable strategy, in alignment with Dawkins, but also partially with my above question. Mutual defection or mutual cooperation, which is the strategy of domination and stable at the same time?

One of the most curious omissions of Dennett is to the iterated prisoner's dilemma. Simply described: as the game is iterated, the players learn from each other, becoming better able to predict the moves of their opponent and choose the optimal response. It could be claimed that this version requires genes to have rationality, but does it? A gene, according to Dennett, will act in whatever manner necessary to guarantee replication. It seems apparent, that even with as-if rationality, a fluid strategy is probable.

While this still reflects Dawkin's and Dennett's view of ESS, in both Dennett's version and the classic version, it begins to shift away from my posited theory, that mutual cooperation is the optimal strategy. Axelrod in The Evolution of Cooperation (1984) proved just this. The strategy of tit for tat (credited to Anatol Rapoport), cooperates on move one and afterwards does whatever the opponent did in the previous round, was pitted against over fifty competing theories in 200 cycles each. It came out on top against all the others. Axelrod repeated his experiment, this time Maynard Smith submitted his theory, a variation of Rapoport's (tit for two tats), and finished in 24th out of 66 entries. Again tit for tat beat all the others.

A case could be made that ESS is tit for tat. Without going into the mathematics behind optimality payoffs, mutual cooperation in the classic game is the optimal choice and the most rational. Mutual defection in Dennett's version is the optimal choice and most rational. The latter supports Dennett's illustration of the mother and the fetus. But turning to species, Dennett's version of the prisoner's dilemma only works at the meta-level.

Taking into account three types of species, the super predators (crocodiles), the predators (tigers), and the non-predators (gazelles), we can assign always defect, defect or cooperate, and always cooperate to them. If we follow Dennett's version, then logically one would have to assume that crocodiles represent ESS at the non-meta level. The tigers are able to mostly represent ESS at the non-meta level. But, the gazelles do not seem to. How can a creature that always cooperates have continued survival against crocodiles and tigers? Of course this is at the intentional level, and the as-if rationality becomes actual rationality.

Returning to the gene level, bringing back to focus the as-if rationality, ESS and Dennett's version of the prisoner's dilemma works as a meta strategy. The genes of all three animals are not
aware of the choices being made at the intentional level, but are driven to defection, adaptation, to increase the chances of replication. The classic prisoner's dilemma seems to not work at the physical level, because that would mean that genes would always cooperate, and theoretically limit the chance for replication. Or more likely, it would mean that adaptation, while still possible, must have another cause, a cause that is at the intentional level.

Therein lies the danger of the classic version. It violates Dennett's reverse engineering. It makes adaptation happen for rational reasons, not as-if ones, and quite possibly plays into Smith's evolutionary stable state, which Gould has run with. Dennett allows for the possibility of stasis in evolution, as does Darwin (Dennett's assertion). But Dennett is quick to point out that stasis is not an end-game, with his thorough explanation of habitat tracking. And it is here that the problem of the super predator dents Dennett's armor.

If the super predator is the optimal player in Dennett's version of the dilemma, always choosing to defect, why is it, that in the course of evolution the super predators become extinct? It goes to reason that if they were able to adapt at the gene level, if their habitat changed, they would follow the shifting habitat, or shift genetically to adapt to their changing habitat. There is little evidence here, but what if they followed Dennett's habitat tracking and still went extinct? That appears to be a strong case against adaptation being driven at the gene level. The super predators, confronted with a shifting habitat, and not being aware at the intentional level of the severity of the change, opting for continued dominance, by intent made themselves extinct. The ESS would have still worked as a meta-strategy at the genetic level, but a rapid change in environment could happen quicker than genetic shift. In this case, Dennett's version of the dilemma still works.

So it appears that if one allows for both versions of the prisoner's dilemma, and for Smith's evolutionary stable state, adaptation is a viable theory. A clarification needs to be made though, that adaptation occurs differently at the physical and the intentional levels. During a period of stasis, both versions of the dilemma work in concert, with genes always defecting, and with species always cooperating. Once the stasis ends though, adaptation determines survival from the intentional level of a species.

At the physical level, adaptation takes the form of the ESS, Dennett's prisoner's dilemma, with genes continually defecting, in order to improve the chance for replication. At the intentional level though, mutual cooperation is the surest form of replication, with species adapting in unison with their environment. Species that are unable to adapt at the intentional level, ones that always defect, classic prisoner's dilemma, Tyrannosaurus rex, go extinct with a shifting environment. While at the physical stance there is sustained adaptation, it can not meet the speed of change required for continual existence. Since the genes are then at the mercy of the intentional level, adaptation at that level is the determinant of survival. No sky hooks are required, only specialized cranes, ones that place intentionality as the foundation in reverse engineering, ones that Dennett seems to have not envisioned in his version of adaptation.

Note: references to Dennett's ideas are from Darwin's Dangerous Idea by Dennett

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