http://www.nature.com/nature/journal/v451/n7175/full/nature06455.html

http://www.nature.com/nature/journal/v451/n7175/box/nature06455_BX1.html

“The coevolution of choosiness and cooperation” from Nature magazine

http://en.wikipedia.org/wiki/Evolutionarily_stable_strategy

Supplementary Wikipedia article: “Evolutionarily Stable Strategy”

The motivation for analyzing choosiness and cooperation between individuals is to seek a better understanding of biological systems and human societies. The interaction that occurs specifically between non-relatives is what the article focuses on.

The way choosiness and cooperation relate to the course is through game theory as applied to the “game of life”, what is described as a special case of the prisoner’s dilemma, which we explored in question 4 of problem set 2. They consider an infinite population, of which two individuals play several rounds in a game termed a “social dilemma.” Traits of a player are divided into two components: one for cooperativeness, x, the amount of effort used to create benefits for a co-player, and one for choosiness, y, the “minimum degree of cooperativeness that the focal individual is prepared to accept from its co-player.” In this model, traits x and y are constant, unaffected by a co-player’s behavior. Their model also gives players a certain payoff per round, W(x,x’), a function of each player’s effort, and intentionally designed to create a conflict of interest, in which each player wants the other to put in most of the effort. (The “prime” symbol refers to the other player.) In receiving the payoff, each player becomes aware of the other player’s effort or cooperativeness. This is the point in the round where the relationship either continues or ends. If each player is mutually acceptant of the other, i.e. x ≥ y’ and x’ ≥ y, then both players stay with each other into the next round if neither dies. However, if one of the above two conditions does not hold, then the pair breaks up and survivors reconvene as a group of unpaired individuals. You can see that if, say, player 2 is not very cooperative and player 1 is very choosy (x’ ≤ y), then this would imply a conflict of interest. New pairs are taken randomly from this group to participate in the next round. This model is much more complex than ones discussed in class. It also considers reproduction, the cost of finding a new co-player, and distinctions between adult and juvenile mortality, all as part of a five-step population cycle model.

As in class, there is a Nash equilibrium solution corresponding to the expected behavior when individuals try to maximize their own payoffs. This can also be called a non-cooperative solution. In addition, there is a cooperative solution corresponding to the expected behavior when payoffs to pairs are being maximized, a solution not covered in class but which involves several concepts that we learned in the first few weeks of the course.

In analyzing this evolutionary game, we seek to identify an evolutionarily stable strategy (ESS), a sort of refinement of the Nash equilibrium such that once it is set in a population, natural selection is enough to bar alternative, or mutant, strategies from pervading. The Nash equilibrium is modified in part to account for the effects of evolution, namely that the rationality associated with Nash equilibria is not appropriate for evolutionary applications. According to Wikipedia, “rational foresight cannot explain the outcomes of trial-and-error processes like evolution.” In this particular game, a good ESS would involve neither cooperativeness nor choosiness, as in the prisoner’s dilemma. This is a stable strategy because being choosy has no payoff in a world where everyone is the same. As a result, there is no incentive to put in more effort than the Nash effort because there is no risk of one’s co-player being unhappy with the matching and deciding to dismiss the other.

What is interesting is that if a means to vary the characteristics of a population, such as a natural process like mutation, is taken into account, the result changes significantly to produce higher and higher levels of cooperativeness. The degree of cooperativeness depends greatly on the degree of variation. There are now advantages in dismissing uncooperative people, because that would increase the availability of cooperative people. This relationship drives up the average level of cooperativeness in a society. One can argue that in response, the standards of a population would rise, meaning that the degree of cooperativeness that is considered “cooperative enough” increases. This would cause an increase in the number of individuals being dismissed for uncooperativeness, which would in turn further increase the levels of cooperativeness, and this process would continue in a positive feedback loop. If the payoff function is set just right, cooperativeness levels will reach the cooperative solution, which is equated to the continuous prisoner’s dilemma.