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 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."

63. The Stag Hunt

Note: This post is the sixty-third 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.

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.

Stimulus Stories

I’ve been doing lots of reading over the last few months, trying to get my head around the current financial meltdown.

In my current thinking, which is likely to change as I continue to try and organize my thoughts, I see three stories that relate to the question of 'should we try to undertake a government stimulus and if so, how big should it be?'

This post lays out those three stories to provide some context for our current economic situation and perhaps sort out some of the different threads of the argument.

Story #1: The Counterweight

In this story, we have an economy that goes through periodic ups and downs. Because we would prefer things to be stable rather than having ups and downs, the government times its discretionary spending to offset these ups and downs.

When times are good, government runs a surplus and dampens economic activity. When times are bad, government runs a deficit and increases economic activity.

It’s a pretty simple story. The main concerns are 1) Does government surplus/deficit have the effect on the economy we think it does? And 2) Will government actually run a surplus during the good times to offset the deficits from the bad years, or will they just accumulate more and more debt.

One positive is that by spending during downturns, government can generally get more bang for its buck since things tend to be cheaper during a downturn. Since these things (like infrastructure spending) need to be done anyway, it is good long term planning to undertake them during downturns as much as possible.

Certain government programs such as welfare and unemployment insurance are called 'automatic stabilizers' because they naturally go up during hard times and go down during good times, providing the sort of counter-cyclical government activity that is desired in the counterweight story.

Given that Canada is in a downturn, this story suggests that a government deficit that will boost the economy during this downturn is a good idea. However, these types of recessionary deficits are usually just the ones that occur naturally when tax revenue falls and government social spending goes up in a recession. We don't normally pile a large additional 'stimulus' on top of the recession caused deficits.


Story #2: The Global Imbalance

In this story, the world is comprised of a number of countries, some of whom, like China, Japan and Germany (the savers), produce a lot more than they consume, some of whom, like the U.S. and the U.K. (the consumers), consume a lot more than they produce, and some, like Canada, that are pretty much in balance.

In order to make the payments balance, the savers use their extra money to buy up the countries of the consumers, investing in their stocks and bonds to generate a return in dividends, capital gains and interest payments. This process, however, can only go so far before it starts to break down and the consumer countries no longer have enough money to keep paying the saver countries the interest and dividends on all the investments the savers have made in the consumers country. Or as more typically happens, you reach a point where the savers get nervous that the consumers can't pay them back so they yank out their money and crash the economy of the consumers.

Eventually, one way or another, the consumers will have to consume less and save more, and vice-versa. Typically, you would expect the currency of consumer nations to fall, making their exports cheaper, their imports more expensive and rebalancing the situation (we can see this happening currently with the fall in the value of the British Pound), but this does not always happen soon enough to prevent a crisis and there can be barriers to this process (for example, savers might peg their currency to the currency of the consumer nation as China does with the U.S.)

In this story, it would be unwise for the consumer nations to take on more debt in an effort to sustain their consumption. It is, instead, the saver nations that should be trying to stimulate their economies so that their own citizens can take up some of the slack when the consumer nations stop living beyond their means.

Given that Canada is relatively balanced between saving and spending, this story has little relevance for us.

Story #3: The Stag Hunt

The Stag Hunt is a 'game' (in the game theory sense), that has the following characteristics:

There are two equilibrium situations:

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.

During the Great Depression, Keynes theorized that the economy resembled the Stag Hunt game (although of course Game Theory had not been discovered yet, so he didn't describe the situation in those terms). The economy had a 'good' equilibrium where people were willing to make risky investments because these had a reasonable chance of making a good return, because everybody else was also making investments, allowing money to circulate and the economy to reach its full capacity.

The Great Depression, per Keynes, reflected a situation where the economy had fallen into a 'bad' equilibrium, where people were too scared to make risky investments, and that because nobody had enough resources to act alone, anyone who did make investments would just lose their money and scare off other would-be investors even more.

In this situation, Keynes reasoned, the only way out was for government, the only entity in society with the necessary resources, to commit itself to doing so much investment that it could carry the economy by itself for a while. This would then encourage others to make investments since they would know that the economy was going to be all right since it was being sustained by government spending.

Once the 'good' equilibrium had been restored, then government could withdraw and allow the economy to continue functioning on its own.

It is as if a mighty hunter appeared who could catch deer by themselves and set off, boldly announcing their intention to do so, knowing that if their claim was credible, and that if deer catching was now seen as assured (or reasonably likely) then the other hunters would all come along to share the bounty. Once all the hunters were happily deer hunting again, the mighty hunter could withdraw and leave them to it, resting his or her weary steed for the next hare-brained crisis.

Under this story, the stimulus needed is not the sort of counter-cyclical balancing described in the counterweight story, but rather a massive, 'shock and awe' style stimulus that is enough to carry the economy almost on its own for long enough to persuade the private sector to join in. The historical view of this story says that it was the massive government spending undertaken to fight World War II that shifted the economy from the 'bad' equilibrium of the Great Depression to the 'good' equilibrium of the post-War years.

So the question for Canada is if we are in danger of slipping into the 'bad' equilibrium (I don’t think anyone would say we were there already). If the answer is yes, then we have a second question – can we pre-emptively stimulate the economy to prevent the transition to the lower equilibrium, or do we need to wait until the 'bad' equilibrium is reached and then try to stimulate ourselves out of it.

One of the risks here is that if the government tries to shift the economy from one equilibrium to another and fails (the people don't believe the government can catch the deer), we will have that much more government debt and be no better off (aside from now having whatever it is the stimulus was spent on). For consumer nations like the U.K. and the U.S., there is the added risk that the government will spook its foreign creditors running up all the extra debt, moving forward a crisis as people scramble for the exits.

Another risk is that it is possible that there were certain weak points in the economy that triggered the transition from 'good' equilibrium to 'bad' equilibrium and that the 'good' equilibrium is not actually an equilibrium any more and can not be achieved, or at least sustained, until those weak spots have been fixed. Based on the run-up to both the Great Depression and our current troubles, likely candidates for such weak points include, at the least, overly high debt levels and income inequality.

Given our current situation, an inadequate supply of cheap energy may be another potential weak point that prevents the 'good' equilibrium from being sustained.


What type and size of stimulus you support for Canada depends to a great extent on which of these (or some other) stories you believe to be operative currently and how you weigh the benefits and risks of each approach.


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A note on game theory, the 'stag hunt' problem is quite similar to the better known prisoner's dilemma. The main difference is that in the prisoner's dilemma, the best possible outcome for an individual is for the other person to cooperate and for you to betray them. In the stag hunt, the best possible outcome is the cooperative one.

The effective difference is that to reach the best overall outcome in the stag hunt game, you only need coordination and trust, whereas in the prisoners dilemma you need coordination, trust AND some additional quality (you might call it 'loyalty' or 'empathy' - or, in a repeated game, 'payback') that makes you feel the pain of the other person so that you choose the overall optimum (cooperation) rather than the personal optimum (betraying the other player).