Game theory and the peacock’s tail


Jason Collins


May 9, 2012

Over at Cheap Talk, Jeff Ely has posted on a presentation by Balazs Szentes at The Biological Basis of Preferences and Behavior conference. Ely writes:

Balazs Szentes stole the show with a new theory of the peacock’s tail. …

Suppose female peacocks choose which type of male peacock to mate with: small or large tails. Once the females sort themselves across these two separate markets, the peacocks are matched and they mate.

The female peacocks are differentiated by health, and within a peacock couple health partially compensates for the disadvantageous tail. In the model this means that healthy females who mate with big-tailed peacocks will produce almost as many surviving offspring as they would if they mated with peacocks without the disadvantage of the tail. …

Consider what happens when a small-tailed peacock population is invaded by a mutation which gives some male peacocks large tails. Since female peacocks make up half the population of peacocks there is now an imbalance in the market for small-tailed peacocks. In particular the males are in excess demand and some females will have trouble finding a mate.

On the other hand the big-tailed male peacocks are there for the taking and its going to be the healthy female peacocks who will have the greatest incentive to switch to the market for big tail. The small cost they pay in terms of reduced quantity of offspring will be offset by their increased chance of mating. The big tails have successfully invaded.

Szentes’s theory illustrates the mixed feelings I expressed in my recent post about some of the presentations at the conference. The model underlying the theory is clever and interesting, but Szentes’s focus is more on the game theory than the evolutionary problem that the model is proposed to address. The model offers limited insight into the evolution of the peacock’s tail as the assumptions underpinning the model do not hold.

First, the model requires an assumption of monogamy, which peacocks are not. As for most males with ornaments, the peacock’s tail is used to attract multiple partners to make up for the handicap that the ornament imposes (as the more established theory suggests). The model also assumes that the males are indifferent as to who they mate with (despite being monogamous), with high quality females unable to attract male interest above that of females of low quality.

Without those assumptions, the findings derived from the model no longer hold. In some respects, the sexes in the model appear backward, as a lack of males willing to give sperm is not an issue in most species. The low investment by males makes females the scarce resource.

I expect that these issues are of less concern to Szentes (or, based on his post, Ely) than they are for me, as his interest lies more in the model than its particular application. Szentes appeared to be aware of these critiques when they were raised at the conference.

If the model is not useful in explaining the peacock’s tail, what situation might the model describe? Instead of talking of disadvantaged males with tails, could we talk of low quality males and use the model to explain the persistence of low quality males in a population? This is an interesting model looking for a use.

*The videos are many of the presentations are now up.