Wednesday, November 30, 2011

Evolution: Part V: Cooperation II: Tit-Fot-Tat

We have seen that sometimes, organisms cooperate because, for each one, it is better than the alternative. But this is not always the case. Sometimes, two organisms are placed in direct competition.
The following material is flagged Green Level. It is intended to reflect material that the author believes to be a matter of consensus among experts in the field. This belief may be incorrect, however; and as the author is not an expert and does not have an expert fact-checking the article, errors may creep in.
So, last time we looked at a population in which cooperation was an undeniable advantage. But what about most other forms of cooperation listed in the article last time? What about times when not cooperating is better for the individual than cooperating?

Let's look at how that works.
  • All other things being equal, it is better for the individual if they do not cooperate.
  • All other things being equal, it is better for the individual if others cooperate with them.
  • All other things being equal, it is better for the individual if all individuals cooperate than no individuals cooperate.
  • If it is possible for individuals to meet more than once, it is better for each for all to cooperate twice than for each to cooperate once and be cooperated with once.
That's right, those of you who were following the game theory Topic. This is the Prisoner's Dilemma. And, if you recall, we have already shown that, in the case where the Prisoner's Dilemma is repeated and no player knows when the final iteration will be, it is to the advantage of each player to cooperate until their opponent fails to cooperate, and then respond in kind.

So what about when each player knows when the game will end?  Well, the behavior described there is consistent with what is observed in nature. If two organisms are cooperating, they will tend to break off their cooperation as soon as one is likely to have been mortally injured.

So, if a population is full of sociopathic individuals, how does this arise? Let's look at how the Tit-For-Tat strategy handles such a population.
In the first generation, Tit-For-Tat plays cooperate on the first turn, and defect on each turn afterward. Thus, Tit-For-Tat is at a marginal disadvantage. But, the selective pressure against a trait at a disadvantage is proportional to how much of a disadvantage it is. Which, in this case, is "not that much", so there's a decent chance that Tit-For-Tat makes it into the next generation.
In the second generation, it is possible for two individuals playing Tit-For-Tat to meet. In this case, these individuals will play cooperate on one another, and react to other individuals as described above. But since each is meeting an individual playing cooperate, the selective pressure is lessened.
In other words, the selective pressure against Tit-For-Tat is inversely proportional to (a strictly-increasing function of) the number of individuals already playing Tit-For-Tat.

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