64. Stag Hunting & Correlation

Note: This post is the sixty-fourth in a series about government and commercial ethics. Click here for the full listing of the series. The first post in the series has more detail on the book 'Systems of Survival' by Jane Jacobs which inspired this series.

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."

60. Signalling

Note: This post is the sixtieth in a series about government and commercial ethics. Click here for the full listing of the series. The first post in the series has more detail on the book 'Systems of Survival' by Jane Jacobs which inspired this series.

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"Buying bread from a man in Brussels
He was six foot four and full of muscles
I said, 'Do you speak-a my language?'
He just smiled and gave me a vegemite sandwich"


In a world where everyone behaves the same way (e.g. the world of most economic models), being able to tell one person from another isn't all that useful. But as we saw a few posts back, and as common sense also indicates, people vary, with some people being more prone to cooperative behaviour than others.

If we imagine ourselves wandering around a world filled with a mix of those who are willing to cooperate with us, and those who will pretend to cooperate just to take advantage of us, then the importance of knowing who you can trust becomes obvious.

One way is to learn by experience. If you can remember who you've dealt with in the past, then you can shun those who've defected against you and only deal with people you've had successful dealings with before. But this still leaves a problem of what to do with people you are meeting for the first time, or people who you are dealing with in a new situation, or even people who defected on you before, but claim to have turned over a new leaf.

In these cases, we tend to look for signs that indicate we can trust someone. Maybe a common language or culture, or skin colour or alma mater, or a certain manner of dress or hairstyle, or a certain level of courteousness, or a certain credit score, or even a certain food choice (e.g. vegemite sandwich).

Thinking more generally, even someone's past behaviour could just be considered another type of signal to take into consideration.

Ideally, the signs that we look for will be hard to fake, since otherwise defectors might just try to pass themselves off as cooperators. Barring the use of memory altering technology, past experience with a person can be very hard to fake, which makes past experience with someone one of the best signals of their potential willingness to cooperate in the future.

Given a perfect ability to differentiate cooperators from defectors, even a group of cooperators as small as just 2 people could outperform a society full of defectors. But given a complete inability to differentiate cooperators from defectors, and lacking a way of keeping track of the results of prior dealings with people, then cooperators would become helpless against defectors - and the defectors will likely take advantage of the cooperators until eventually there are no cooperators left.

As we covered a while back, this distinction is what led David Gauthier to assume, in Morals By Agreement that people pursuing cooperation would be able to perfectly differentiate cooperators from defectors.

This is all pretty straightforward common sense, but as this series goes along and I talk more about how cooperative behaviour can evolve (or go extinct) in various circumstances, it will be useful to keep some basic points in mind, such as the importance of signalling cooperative intentions and remembering past interactions with people in sustaining cooperation.

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A few other notes on the topic of signalling:

It's worth mentioning that signalling is only necessary when one party to a transaction has information that another party lacks (the information that will be signalled) so, from an economic perspective, situations requiring signalling are an example of one of the effects of asymmetric information , a topic which we discussed here a while back.

Of course, barring an ability to read minds or predict the future, you never really know for sure what the other person is going to do, so in that sense every transaction involves asymmetric information, which is a bit hard on economic theories which rely on the absence of asymmetric information as a key assumption.

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Signalling problems can also be tied back to game theory via various 'signalling games' which investigate what messages might be sent and received between players under varying circumstances.

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Some concepts related to the idea of signalling:

Cheap Talk - Signs that can be made with little effort and thus don't signify much. For example, if I ask you, 'Are you going to screw me over?' And you say, 'No', your answer would qualify as cheap talk, since it doesn't cost you much to make that statement. Or if cooperators tried to identify one another by wearing a yellow shirt, than anyone could wear a yellow shirt and pretend to be a cooperator. This notion is generally captured in the expression, 'actions speak louder than words' - since actions typically have a higher cost than words do.


Common Knowledge - Something that everybody knows, and everybody knows that everybody knows, and everybody knows that everybody knows and everybody knows, and so on. The Stanford Encyclopedia of Philosophy provides an example:

"A proposition A is mutual knowledge among a set of agents if each agent knows that A. Mutual knowledge by itself implies nothing about what, if any, knowledge anyone attributes to anyone else. Suppose each student arrives for a class meeting knowing that the instructor will be late. That the instructor will be late is mutual knowledge, but each student might think only she knows the instructor will be late. However, if one of the students says openly 'Peter told me he will be late again,' then each student knows that each student knows that the instructor will be late, each student knows that each student knows that each student knows that the instructor will be late, and so on, ad infinitum. The announcement made the mutually known fact common knowledge among the students."