91. Another View on the Evolution of Cooperation

Note: This post is the ninety-first 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.

I happened upon an interesting article the other day by Daron Acemolgu.

Acemolgu points out that researchers often use coordination models to study the level of cooperation in society because these models allow for multiple equilibria - i.e. one with cooperation, one without¹

"Why do similar societies end up with different social norms, and why and how social norms sometimes change? A common approach to answering these questions is to use coordination games, which have multiple equilibria corresponding to different self-fulfilling patterns of behaviour and rationalise the divergent social norms as corresponding to these equilibria. For example, it can be an equilibrium for all agents to be generally trusting of each other over time, while it is also an equilibrium for no agent to trust anybody else in society. We can then associate the trust and no-trust equilibria with different social norms."

As he goes on to point out, this isn't a very dynamic analysis, in the sense that it doesn't answer the questions of why or how we get from one equilibrium to another.

"Simply ascribing different norms to different equilibria has several shortcomings, however. First, it provides little insight about why particular social norms and outcomes emerge in some societies and not in others. Second, it is similarly silent about why and how some societies are able to break away from a less favourable (e.g., no trust) equilibrium. Third, it also does not provide a conceptual framework for studying how leadership by some individuals can help change social norms."

I didn't spring for the $5 required to download the full paper, but from the article it seems like one mechanism posited by Acemolgu for society to move from one equilibrium to another is if a 'prominent' person influences other people with their own behaviour.

"A particularly important form of history in our analysis is the past actions of "prominent" agents who have greater visibility (for example because of their social station or status). Their actions matter for two distinct but related reasons. First, the actions of prominent agents, impact the payoffs of the other agents who directly interact with them. Second, and more importantly, because prominent agents are commonly observed, they help coordinate expectations in society. For example, following a dishonest or corrupt behaviour by a prominent agent, even future generations who are not directly affected by this behaviour become more likely to act similarly for two reasons; first, because they will be interacting with others who were directly affected by the prominent agent's behaviour and who were thus more likely to have followed suit; and second, because they will realise that others in the future will interpret their own imperfect information in light of this type of behaviour. The actions of prominent agents may thus have a contagious effect on the rest of society."

What strikes me, coming back to the discussion about coordination, is all the words we have that, in the right context, mean the same thing: coordination, cooperation, correlation, collaboration, etc. Naturally, the trick with a coordination problem is to somehow coordinate everyone's behaviour. A hierarchical structure can create a monopoly in which one entity/person controls all, thus greatly simplifying the problem of getting everyone to sing from the same songbook. When putting leviathan in charge isn't feasible or isn't desired, then it becomes trickier to get a bunch of independent actors to coordinate on a particular outcome.

The 'prominent' person is like a soft version of the leviathan - not forcing everyone to go along, merely setting a good or bad example and hoping the ripples of that behaviour are enough to 'tip' society from one equilibrium to another. I didn't read the paper so I shouldn't really comment, but the notion that something like JFK asking people what they can do for their country is going to lead to a widespread change in behaviour seems hard to swallow for me. To me it seems more likely that levels of cooperation will be driven by a combination of history (as Acemolgu acknowledges) and changes in fundamental factors like technology (e.g. the medium is the message) and the natural environment (along the lines that I discussed in my last post).


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¹Note: The Stag Hunt, that we discussed back here is an example of a game theory model with more than one equilibrium.

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."

63. The Stag Hunt

Just a short post this week, more of an intro to next week's post than anything else. I covered most of this ground back here, but I wanted to formally include it in the series on ethics.

We've talked a lot here about the Prisoner's Dilemma, but another type of interaction / game that comes up when talking about ethics is the 'Stag Hunt.'

Wikipedia summarizes the Stag Hunt as follows:

"In game theory, the stag hunt is a game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.

The stag hunt differs from the Prisoner's Dilemma in that there are two Nash equilibria: when both players cooperate and both players defect. In the Prisoners Dilemma, however, despite the fact that both players cooperating is Pareto efficient, the only Nash equilibrium is when both players choose to defect."

Here's an example:

                                        Adam
                              Stag                    Hare
Eve          Stag:      [2,2]                 [0,1]
                 Hare :     [1,0]                [1,1]

Unlike in the Prisoner's Dilemma where Adam's best choice would be to defect (hunt Hare) no matter what Eve does, in this case, Adam's response depends on what Eve is doing. If Eve is cooperating (hunting Stag) then it makes sense for Adam to hunt stag (cooperate as well). If Eve isn't going to cooperate, then Adam shouldn't cooperate either.

You can see how this dynamic sets up the two equilibiria that Wikipedia mentioned:

1) A 'good' equilibrium where hunters catch deer, the most valuable game animal in the forest. Because the deer is elusive, catching it requires cooperation between the hunters.

2) A 'bad' equilibrium where the hunters don't cooperate, and are not able to catch the deer so they catch rabbits instead, which can be caught without cooperation, but are not as tasty and meaty as deer. Mmm, venison.

In the 'bad' equilibrium, the hunters know they could do better by working together to catch a deer, but because nobody can act on his own (you can't catch the deer without help) and because they can't be sure that if they go to hunt deer that others will help, it is safer to just catch rabbits, rather than going off by yourself to catch the deer, having nobody help you and ending up with nothing.


The description of the Stag Hunt - where you should cooperate if the other person does and defect if they do - may also sound reminiscent of the Tit for Tat strategy that performed so well in the repeated Prisoner's Dilemma tournaments that Robert Axelrod described in 'The Evolution of Cooperation'. This isn't a coincidence - having a Prisoner's Dilemma repeat over time and having the participants switch to defection if the other player defects, transforms the payouts from A Prisoner's Dilemma into the payouts from a Stag Hunt.

Basically, what happens is that the gain a person gets from betraying the other player in the first Prisoner's Dilemma is more than offset by the losses that follow because the other player is never again willing to cooperate with you. Taking this potential future loss into consideration, it becomes in your best interest to cooperate now - if you expect the other player to cooperate.

This last part is the rub with the Stag Hunt, and you can see why it is also sometimes known as the 'Assurance Game' - if you could only assure the other player that you were going to cooperate (maybe by signing a contract, shaking hands, or by maintaining a high seller rating on ebay, etc.) then it would be in their interest to also cooperate.

In a way, the Stag Hunt is like a stepping stone on the road from the hopeless one-time Prisoner's Dilemma style interaction, to an outcome of mutually beneficial cooperation.

It's not just the possibility of the Prisoner's Dilemma repeating that can transform the interaction into a Stag Hunt, a moral principle that places merit on being 'nice' in the sense that Axelrod used it - starting off by cooperating with people, and only stopping cooperation if the other player betrays you first - could also change the payoffs in the Prisoner's Dilemma so that they resemble the Stag Hunt instead.

More on the Stag Hunt next week.