15 January 2010

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.

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