64. Stag Hunting & Correlation
Note: This post is a continuation from last week's post on the Stag Hunt.
This week, I'm going to talk about the book, "The Stag Hunt and The Evolution of Social Structure," by Brian Skyrms.
Skyrms argues that the Stag Hunt is a better model of the challenge of human cooperation than the Stag Hunt. Whereas the Prisoner's Dilemma only has one equilibrium solution (everyone defects), the Stag Hunt has two possible equilibriums, everyone cooperates (hunts stag) or everyone defects (hunts hare). He argues that this better reflects the notion of a social contract which can either not exist (state of nature) or exist (society).
The primary theme of the book is Skyrms' argument that they key to achieving cooperation in the stag hunt is correlation. By correlation he means that those who are disposed to stag hunting (cooperation) must find a way to work together and avoid the hare hunters (defectors). This is a similar point to the one Axelrod made, but Skyrms goes into more detail. Note that, implicit in this argument is an assumption that there are two sort of people out there, stag hunters (cooperators) and hare hunters (defectors).
The first method of improving correlation that Skyrms looks at is location.
One of the interesting aspects of this book is the rich use that Skyrms makes of biological examples for how cooperation is far from a distinctly human characteristic. For example, his opening to the chapter on location,
"One strain of E Coli bacteria produces a poison , to which it is immune, that kills competing strains. It takes resources to produce the poison, and the strain that produces it pays a cost in reproduction for the privilege of killing competitors. If the poisoner strain evolved from a more peaceful strain of E Coli, how did it get started? A few mutant poisoners would cause little change to the average fitness of a large peaceful group ... If a few mutant poisoners are added to a well stirred culture of peaceful E Coli, the mutants are gradually eliminated.
But when the same experiment is performed on agar plates rather than in a well-stirred solution, the poisoners can invade and eventually take over the population. ... I won't tell the full story here, but I hope that I have told enough to illustrate the importance of spatial structure, location, and local interaction for evolutionary dynamics."
It requires energy to move matter from one place to another, so all else equal, people (and animals) don't move more than they have to. If people who are willing to cooperate rather than defect (stag hunters) are clustered rather than dispersed at random, then they will tend to have more interactions with each other - interactions where their cooperative behaviour will pay off. This is pretty much common sense - You can imagine that a group of, say, rebel soldiers is more dangerous if they are all located in one area than if they are thinly scattered across a country - but it's still interesting to see some of the underlying theory that explains why a cluster of like-minded people (or bacteria) can be so effective.
Skyrms' approach throughout the book is to run simulations where he takes a set of agents and lets them interact over time, playing either Stag Hunt or some other game against each other. There are different dynamics allowing the situation to change over time. Sometimes Skyrms has people choose a strategy which will be the best response to the sort of person they expect to encounter (if they expect a hare hunter, they will hunt hare too, and the same for stag hunting). Other times Skyrms has people choose to imitate the strategy of those around them that are performing the best.
In running simulations to test the influence of location on the spread (or demise) of cooperative behaviour in a population, Skyrms tried one-dimensional setups (everybody is in a line) and two dimensional setups (people interact on a grid) and also tried both a 'best response' type of strategy evolution and a 'imitate the best' type of strategy evolution. What he found was that the two dimensional model and the 'imitate the best' approach had the most favourable outcomes for cooperation (Stag Hunting).
But in general, the effect of taking into consideration location (having people interact with their neighbours), rather than just assuming that people interact randomly with each other was that simulations with location as a factor were more favourable to the evolution of cooperation. Note that is consistent with Axelrod's findings as well.
The second method of improving correlation between cooperators that Skyrms looks at is signalling (which we discussed a few posts back).
He describes how a myxobacteria known as Myxococcis xanthus engage in coordinated attacks on larger microbial prey, by making use of quorum signalling - a signal that tells the bacteria when there are enough of them gathered in one place to launch a successful attack. As Skyrms notes, "Myxococcis xanthus has solved the problem of the Stag Hunt."
On the topic of signalling, Skyrms explains how situations where the provision of a signal can lead to mutual benefit result in quick convergence to a mutually recognized set of signals - even when there is no communication between parties (other than the signals) and there aren't any initial cues to suggest what each signal might mean to either side.
Even in cases where there are parties that might benefit from sending out a false signal, and it does not cost anything to send out a false signal (what game theorists call 'cheap talk') the possibility of sending signals can still lead to more cooperative outcomes than might be achieved if signals weren't available to be used.
The third method of correlating cooperative behaviour that Skyrms looks at is through allowing the structure of interaction itself to change. If we let people choose for themselves who to interact with, then stag hunters will typically quickly learn to interact with other stag hunters. Allowing this sort of self-selection is a powerful tool that allows the cooperators to self-select into a club whose members benefit much more than any of the hare hunters that are excluded.
Skyrms concludes by summarizing the results of the various simulations that make up most of the book, and what they tell us about how stag hunting (cooperation) can arise in a population of hare hunters (defectors) over time (given that interactions between people follow a stag hunt type model),
"Over time there is some low level of experimentation with Stag Hunting. Eventually a small group of Stag Hunters comes to interact largely or exclusively with each other. This can come to pass through pure chance and the passage of time in a situation of interaction with neighbors. Or it can happen more rapidly when stag hunters find each other by means of fast interaction dynamics. The small group of stag hunters prospers and can spread by reproduction or by imitation. This process is facilitated if reproduction or imitation neighborhoods are larger than interaction neighborhoods. As a local culture of stag hunting spreads, it can even maintain itself in the unfavorable environment of a large random-mixing population by the device of signalling."