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).


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

75. The Strategy of Conflict Part 1, Deception and Tradition

Note: This post is the seventy-fifth 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.

This week's post is about the book, "The Strategy of Conflict" by Thomas Schelling.

Writing in the 1960's, Schelling was concerned that the field of game theory was too focussed on zero-sum games (games where one person's gain is another's loss - think chess). He proposed a continuum of games, with a pure zero-sum game at one end, and a pure coordination game (where both people gain if they make the right choices and both lose if they don't - think charades) at the other, with 'mixed-motive' games in the middle. At the zero sum game end of the spectrum, participants in the game have negatively correlated outcomes (what's good for me is bad for you) while at the coordination end, they have positively correlated outcomes (what's good for me is good for you as well).

Schelling recognized that in the zero-sum game, deception and secrecy was the order of the day, while in the coordination game, open, forthright communication (honesty) was the key to success.

In the coordination game, Schelling offers a list of examples of how people will find a way to coordinate even when they can't communicate directly with one another:

"Name 'heads' or 'tails.' If you and your partner name the same, you both win a prize.

Circle one of the numbers listed in the line below. You win if you all succeed in circling the same number.

7 100 13 261 99 555

..."

These are the first two in a list of examples that show that when people need to agree on something without communicating, they focus on whatever they think will be the most obvious element to everyone ('heads' because it is written first, '7' because it is the first number in the list, in a later example, dividing a territory along a river since it is the most notable feature of the landscape.)

Later on, Schelling introduces games where the two participants must divide something between themselves. Attacking the other participant can lead to a gain for yourself, but reduces the total amount to be divided. The participants overall do best when they can identify some agreeable way to divide the pie without fighting, but individual participants do best if the agreement is made to suit them.

Schelling theorizes that in situations of this nature, tradition can play a powerful role in providing a focal point that people can agree on. Any attempt to break with tradition re-opens all the contention for position of the various parties involved and can lead to conflict and poorer results for all unless a new tradition can be quickly established¹.

Says Schilling, "We have now rigged the game so that the players must bargain
their way to an outcome, either vocally or by the successive moves that they make, or both. They must find ways of regulating their behaviour, communicating their intentions, letting themselves be led to some meeting of minds, tacit or explicit, to avoid mutual destruction of potential gains. The 'incidental details' may facilitate the players' discovery of expressive behaviour patterns; and the extent to which the symbolic contents of the game - the suggestions and connotations - suggest compromises, limits and regulations should be expected to make a difference.

It should, because it can be a help to both players not to limit themselves to the abstract structure of the game in their search for stable, mutually nondestructive, recognizable patterns of movement. The fundamental psychic and intellectual process is that of participating in the creation of traditions"

In 'Systems of Survival' Jane Jacobs, while not using the language of game theory, expressed a similar speculation about the role of tradition,"I suspect one reason revolutionary governments have become cruel so easily and swiftly after ascendancy is that they've lost the brakes of tradition."

If there wasn't the same potential in the situation for destructive conflict, then agreement, and tradition, wouldn't need to carry the same premium, but in situations where there is potential for a costly back and forth battle, it's better to reach some agreement than none at all - and the bargaining can come down to who can identify a 'traditional' settlement that favours their interests.

That's as far as I've got so far in 'The Strategy of Conflict' but even if there is nothing else interesting in the rest of the book, it's been worthwhile.

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¹ For an example of how angry people can get with even a trivial break in tradition, consider the reallocation of a small amount of downtown Vancouver traffic right of way from cars to bicycles and just how angry this break with the 'all cars all the time' tradition has made people, leading to what one of the few sane articles written about the change accurately described as 'an outpouring of spectacular gibberish' - the gibberish makes more sense if you understand the enraged car drivers as being worried that once tradition has been broken in this fashion, who knows where it will lead or when it will stop.

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.

61. The Evolution of Cooperation (part 1 of 2)

Note: This post is the sixty-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.

The Evolution of Cooperation is the title of perhaps the most famous book on the Prisoner's Dilemma, and possibly Game Theory in general, ever written - by Robert Axelrod.

Reading it again, for the first time in a long time, I could see why it is so popular - it manages to cover a lot of ground with very clear, accessible prose.

The Evolution of Cooperation starts off by recounting a famous game theory tournament. Participants were invited to submit a strategy or 'rule' that would play a Prisoner's Dilemma against strategies submitted by other people. The strategies would be paired up against each other in turn and would play a repeated Prisoner's Dilemma against each other for a certain number of times. The goal was to achieve the highest possible point total, adding up across the matches against all the other strategies.

Recall that the nature of the Prisoner's Dilemma is such that, no matter what action your opponent takes, you will maximize your own total by defecting rather than cooperating. But by changing the situation from a single game to a repeated game, and by allowing participants to retain a memory of what happened before and by allowing them to clearly identify who they were playing against, the tournament introduced a strong signalling element into the Dilemma.

The tournament was won by the simplest strategy submitted, a strategy known as 'Tit For Tat.' Tit for Tat started off by cooperating (Axelrod refers to strategies that start by cooperating as 'nice' strategies), and then each round it just reacts to what the strategy it is matched up with did the previous round. If the strategy it is playing with defected on the last round, Tit for Tat defects this round, and if the strategy it is playing against cooperated on the last round, Tit for Tat cooperates this round.

After the results of the first tournament were published, a second one with more entries was held, but Tit for Tat again turned out to be the winner.

Strategies aren't fixed over time, and people might change their approach if they see another approach that is working better. Or those using a poor strategy might die out (or get fired) and be replaced by someone with a better strategy. Or some people may simply decide to try a new approach that they thought up. Through these sorts of mechanisms, the distribution of strategies, or rules, being used in the population can evolve over time.

An evolutionarily stable strategy is one that, even if everybody in a population is using it, can't be invaded by some other strategy designed to take advantage of it. Axelrod notes that a population where everybody defects is evolutionary stable because it is not possible for anyone playing any sort of cooperative strategy to invade (because they never meet anyone who will reciprocate their cooperation). But even a small cluster of cooperators can invade a much larger population of defectors if the conditions are right (because they will do well enough cooperating with each other to offset their poor results against the defectors).

But the converse is not true. A population where everybody plays a nice strategy like Tit for Tat can't be invaded by an 'Always Defect' strategy, because the Tit for Tats will do better playing each other than the 'Always Defect's will do playing with each other. This is a hopeful result (for those who like to see cooperation) since it suggests that a cooperative equilibrium is more stable than a defective one and that even a small group of cooperators can sometimes thrive in a sea of defectors.

Based on the results of the tournaments, and the success of Tit for Tat, Axelrod offers the following suggested courses of action for doing well in a repeated Prisoner's Dilemma type situation:

1) Don't be envious

As we saw before, envy can transform an absolute gain into a relative loss and a positive sum situation into a zero-sum situation. A common theme throughout the book is the distinction between absolute gains, made possible by the non zero-sum nature of the Prisoner's Dilemma, and zero-sum situations where only relative gains are possible.

2) Don't be the first to defect

'Nice' rules which don't defect first, will do well when playing with each other. This means that 'Mean' rules which defect first, will end up with lower scores against 'nice' opponents than 'Nice' rules do.

3) Reciprocate both cooperation and defection

A failure to reciprocate cooperation leads to unnecessary defection on both sides. A failure to reciprocate defection (by defecting in return the next round) leads to being taken advantage of.

4)Don't Be Too Clever

Unlike in a zero-sum game where you don't want your opponent to have any advantage, in a Prisoner's Dilemma it is important that those who are willing to cooperate recognize that you are willing to cooperate as well. Tit for Tat is a simple rule that helps other rules understand what they are dealing with and act accordingly. And since the best plan when facing Tit for Tat is to cooperate, rules will generally cooperate when they figure out that is the rule their opponent is using.

* * *

Moving along, Chapter 4 shows that friendship is not necessary for cooperation to develop by recounting the story of the 'live and let live' system that developed in the trenches during World War I where enemy units would cooperate by not killing each other, while facing off with each other across the same piece of ground for months at a time.

Chapter 5 shows that even creatures with very limited intelligence (e.g. bacteria) can engage in cooperation in Prisoner's Dilemma type situations. It also theorizes that the cooperation born from Kin Selection (the notion that it makes sense for us to evolve so that we are willing to make sacrifices for those we share genes with) might have provided a foothold of cooperation that could have spread into the sort of reciprocal tit for tat cooperation that would extend across larger groups of people, regardless of whether they are related or not.

I'll cover the rest of 'The Evolution of Cooperation' and talk about some of the implications of the ideas covered in it in next week's post.

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.

* * *

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.

* * *

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.

* * *

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."

55. One Thing Leads to Another

Note: This post is the fifty-fifth in a series. 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.

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In a world where everyone is the same and they all just pursue their own self-interest with no regard for what happens to other people, the question of what happens when people with different preference types interact doesn't arise.

But my last post raised the possibility that people might have different 'temperaments' with respect to how they personally are affected by the fate of the people they deal with. As Alan anticipated in the comments on the last post, if there are different sorts of people potentially out there, then a natural question is to try and see what happens if the different types interact with one another and how a collection of different types of people might change over time.

One of the best known ways that a population makeup can change over time is via evolutionary dynamics. People who are more 'successful' with their actions will have more children than those who are less successful, meaning that, over time, more successful strategies will come to dominate.

A common debate in the social sciences is then whether unselfish behaviour can sustain itself over time, given that selfish people might be able to take advantage of the unselfishness of the altruists. It's true that a group of unselfish people will likely outperform a group of selfish people, but then won't the unselfish group fall victim to selfishness from within? The answers are (as usual) it depends, but I won't get into the details any more in this particular post (with a 2 hour episode of wipeout on tonight, time for posting is limited!).

Evolutionary dynamics are not the only way for a population makeup to change over time. Imitation works too. The Czech Republic (for example) isn't a capitalist country because it was outbred by capitalist countries, it's capitalist (arguably, at least) because the population decided to imitate what they felt was a more successful method of doing things. At a personal level, people will imitate what they other people doing around them if they feel those people are successful (see also Bubble, Housing).

A third option is migration. If people are able to move from one society to another, their movements will alter the distribution of preference types within each society. A constant migration of unselfish types to an unselfish society might offset a trend towards successful acts of selfishness within that society, for example.

A fourth mechanism is that the people themselves do not change, but their relative strength of influence does. Maybe an unselfish society contains only one selfish person, but if that person uses their unchecked greed as a means to taking control of the whole society, then the society could change dramatically despite nobody changing their particular nature.

No doubt there are other mechanisms by which the makeup of preferences in a society can change over time - I can't think of any at the moment, but feel free to point them out in the comments.

This is all pretty abstract, but the point is that it would theoretically be possible to model or simulate various ways in which a society of people with different preference types might evolve over time, applying different mechanisms by which behaviours might spread or change or change in influence over time. There are folks out there who have undertaken this sort of work, and I'll cover some of their efforts in future posts.

20. Morals By Agreement, Chapter 3: Strategy (Game Theory)

Note: This post is the twentieth in a series. Click here for the full listing of the series.

This is the second of what should be a few posts on the book Morals by Agreement, by David Gauthier.

In the last post, we covered chapter 2 of Morals by Agreement, where Gauthier sketched out his view of what it meant for people to behave 'rationally' in situations which didn't involve other people who might themselves be trying to act rationally and whose actions might depend on our actions and vice-versa.

So in chapter 3, Gauthier extends his model of rational behaviour to cover what he refers to as 'strategic interaction' - that is situations where people are interacting with each other, rather than acting on their own. Basically, in the terms I used earlier in this series, he is moving from rational actions, to rational transactions.

The formal branch of knowledge that studies transactions is Game Theory. The most famous game in Game Theory is the Prisoner's Dilemma, which I introduced earlier in the series here.

For more background on game theory here is the Wikipedia entry on game theory and here is the excellent Stanford encyclopedia of philosophy entry on game theory.

When it comes to game theory, examples are the way to go to gain understanding.

Consider a simple game, where Harold and Kumar are trying to meet up at a local restaurant for a meal, but they are not in communication with each other. However, they both know that there are only two restaurants in town, White Castle and Black Castle. Furthermore, they know that Black Castle is closed.

                                        Harold
                            White                     Black
Kumar   White:      [5,5]                 [3,0]
                 Black :     [0,3]              [2,2]

The best outcome is if they both meet at the White Castle (5 for both). For both Harold and Kumar, the next best option is if they go to White Castle and the other person goes to Black Castle - they don't get to meet up, but at least they can eat. For both players, the third best is to meet at Black Castle and the worst option is to go to Black Castle while the other person has gone to White Castle (alone AND hungry).

Gauthier defines rational behavior in transactions, or 'strategic interaction' as follows:

A)Each person's choice must be a rational response (i.e. utility maximizing) to the choices she expects the others to make
B) Each person must expect every other person's choice to satisfy A
C) Each person must believe her choice and expectations to be reflected in the expectations of every other person.

So in the example above, Harold figures that if Kumar goes to White Castle, he (Harold) is better off going as well. But even if Kumar doesn't go to White Castle, Harold is still better off going to White Castle. So condition A sends Harold to White Castle. Condition B tells Harold that Kumar will follow a similar logic and also end up at the White Castle.

The outcome where Harold and Kumar both go to White Castle is what is known in game theory as an equilibrium outcome. What this means is that, given that both Harold and Kumar are choosing to go to White Castle, there is no reason for either of them to unilaterally change their choice. Compare that with the situation where Harold is going to White Castle and Kumar is going to Black Castle - this is not an equilibrium because in this situation, Kumar would be better off to change his strategy.

Now let's look at a different type of game. Consider the question of what side of the road to drive on. For now, imagine that only two people live on a road, Adam and Eve, and they need to agree on which side of the road to drive on and they both own British cars that were designed for driving on the left side of the road.

                                        Eve
                            Left                     Right
Adam   Left:      [2,2]                 [-10,-10]
            Right :    [-10,-10]            [1,1]

Note that there are 2 equilibrium outcomes in this game, One where both drive on the left and both drive on the right. Even though both Adam and Eve are better off if they both drive on the left, if for some reason they are currently both driving on the right, neither has an incentive to unilaterally change their strategy. Only by working together could they shift from the sub-optimal equilibrium to the optimal equilibrium. Unsurprisingly, this type of game is known as a coordination game, where the coordination needed has two parts: 1) making sure that both people pick the same outcome and 2) making sure the equilibrium they end up in is the optimal one.

But what if we change the game slightly so that Adam has a car that is designed to drive on the left and he has always driven on the left so strongly prefers driving on the left. Meanwhile, Eve has a car that is designed to drive on the right, but she just got her license so she is less attached to driving on one particular side.

                                        Eve
                            Left                     Right
Adam   Left:      [5,2]                 [-10,-10]
            Right :    [-10,-10]            [2,3]

Again there are 2 equilibriums and Adam and Eve need to coordinate to make sure they drive on the same side of the road. But the situation is complicated now by the fact that Adam prefers the 'drive on the left' equilibrium and Eve prefers the 'drive on the right' equilibrium.

This now becomes a bargaining problem, one that has been much studied and argued over in the history of game theory. The reason I bring it up here is because Gauthier himself brings it up in chapter 3 - because it will be useful to him later on in the book.


Finally, I won't go over the Prisoner's Dilemma again, but it is worth noting (as Gauthier does) that in the Prisoner's Dilemma, the equilibrium that Gauthier's rules for rational behavior lead to is different from the (Pareto) optimal outcome. In other words, if people pursue their own utility maximization it will lead to sub-optimal outcomes where there are possibilities to make people better off without making anyone worse off, but these possibilties are placed out of reach by people's self-interested behaviour.

Gauthier will argue that morality consists of the constraints necessary to generate optimal outcomes for 'rational' people.

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).