Dennett and Game Theory: Voodoo Mathematics?

Dennett's use of game theory (Dennett, Daniel C. (1995) Darwin's Dangerous Idea: Evolution and the Meanings of Life, New York: Simon & Schuster Paperbacks) as either an explanation or a support for adaptationism is curious. Game theory in evolutionary study seeks to understand the mathematics behind the moves taken by an organism (rational or bounded rationality) to explain why some organisms survive while others do not. Dennett surely has given himself to this mode of explanation, and
ascribes also to defection over cooperation. While he makes allowances for instances where mutual cooperation is the norm, he weighs heavily on the side of defection. It is in this instance where the curiosity comes. Can mutual defection explain an organism's continued existence?

A basic idea of game theory is that when a player is given two choices, to defect or to
cooperate, the most rational choice is made, based on a payoff matrix. In a perfect world, the player will choose the optimal path, mutual cooperation. But since the game is played against other rational players, the optimal is not always the best choice, but the suboptimal one. Anticipation of the moves of the other player enter into the decision-making process. At the human level this involves emotional guesswork and greed, and a learning curve of the opponent's most-likely move. In short, the Prisoner's Dilemma.

A player knowing that mutual cooperation is the optimal choice will not always make
that choice. This is because his opponent may choose to defect, and the resultant would be for the player that chose to cooperate, would have a great loss. It is this knowledge that leads to the suboptimal decision to mutually defect. The players acknowledge that there will be a minor loss on both parts, but neither player will achieve advantage over the other. Stasis at the suboptimal is the norm, whether it is the Evolutionary Stable Strategy or the Nash Equilibrium.

Dennett uses a quote by Dawkins (254) to illustrate his stance on game theory, in that,
an organism “seeks” to dominate its population. This domination is the suboptimal mutual defection of the Prisoner's Dilemma. The organism allows for a minor loss by selecting defection, while taking the chance that its “opponent” will choose to cooperate, thereby enhancing the payoff for the organism that defects. This is akin to the nuclear arms race. The US and the Soviet Union stockpiled weapons, thousands more than necessary, to reach a state of potential mutual obliteration. Both sides chose mutual defection as their strategy, with the side-hope that their opponent would eventually make the choice of cooperation at the wrong moment.

Dennett allows for mutual cooperation, under the correct circumstances. One must
assume that by this he means an abundance of resources, or a period of stasis, one which would not give an organism a large payoff if it chose to defect. Of course, this is then game theory working at the optimal level. But since both Dennett and Dawkins adhere to organisms needing to dominate their population, the optimal level is most-likely a short-lived state (dozens, hundreds of generations?). This is what Dennett refers to as “evolutionary unenforceable” states (256). In short, Dennett believes that unselfish states, mutual cooperation, “must be designed (256)”. It is here that Dennett swings the optimal state, mutual cooperation, into the field of aberration.

Dennett goes further to state that cooperation is exceedingly rare in nature. The trees
grow tall because they are “selfish”, and as such, organisms benefit from this selfishness. Without tall trees, selfish trees, “beautiful forests...could not exist (256)”. Dennett acknowledges that this is a damning view of evolution. It is not because it is loathsome, but because it equates all organisms to selfish desires, conscious or not. In general, if an organism can succeed by taking an advantage over another organism, it will. Mutual defection is the norm, not the exception.

This state is beautifully illustrated in Hofstadter's Wolf Dilemma (Hofstadter, D.R.
(1985) Metamagical Themas: Questing for the essence of mind and pattern, New York: Basic Books, Inc.). Basically it is a modified Prisoner's Dilemma, but with a much larger payoff for mutual cooperation. Hofstadter invited twenty friends to submit their rational choice, one without emotional baggage, to him. The payoffs were skewed towards mutual cooperation. In short, if everyone chose mutual cooperation, they would receive a larger payoff ($57) than if they all chose mutual defection ($19). Dennett himself participated in this experiment and chose mutual cooperation. His choice was the minority choice. At the end, 70% of the participants chose to defect.

So it seems that defection is a kind of ingrained rationality. The question must be
raised though, that if selfishness is a norm, is this not anthropomorphising organisms? Can we equate a human emotion to the selection process of a gene? While it is a stretch, there does not seem to be any other explanation as to why mutual defection appears to be the rule. Selfishness appears to be a genetic predilection.

Gould has brought about the idea of hidden constraints, ones that seemingly effect game theory, and in his view it seems, invalidates game theory as it applies to adaptation (257). Dennett makes the point that adaptationists already allow for hidden constraints. A hidden constraint is one that limits the choices of an organism, with or without conscious knowledge of the constraint. Dennett makes the case of a butterfly that is perfectly camouflaged on the forest floor (260). The butterfly dominates other butterflies because of its coloration advantage. But as Dennett points out, if the forest floor were to change, the butterfly would either adapt or not, and if it does not “it will find some other adaptation in its limited kit of available moves or it will soon disappear (260)”. This is a hidden constraint and not necessarily counter to game theoretic approach.

Here is where Dennett ties hidden constraints to game theory, and brings it all into the
adaptationist's fold: hidden constraints allow for all possible “habitable” moves, and as such, falls within the realm of game theory. Selfish intent is only constrained by what is possible. In a sense, this is not a constraint at all. How could anything choose to move in an impossible way? And even if it could somehow make the impossible possible, could it survive? Would an organism that exists in an oxygen breathing world benefit from being able to breathe nitrogen? Surely it would be a mutant and if it lost it's ability to breathe oxygen, it would become extinct.

In the end, Dennett has done a remarkable job at tying game theory to adaptationist
evolutionary theory. While his ideas are not without their detractors, he seems to have built what can not be successfully assailed. Selfishness, whether conscious or unconscious, are merely gears in the machine of design. It is the “intent” of organisms to take advantage of all possible habitable moves, within the constraints of possibility, to adapt. It is an either/or position. Either an organism adapts, or it does not. If it does not, it will tend towards extinction, it will be the player that chooses to cooperate in a field of defectors.

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