1996 Penguin books
In
Puccini's opera Tosca, the heroine is faced with a terrible dilemma. Her
lover Cavaradossi has been condemned to death by Scarpia, the police chief, but
Scarpia has offered her a deal. If Tosca will sleep with him, he will save her
lover's life by telling the firing squad to use blanks. Tosca decides to deceive
Scarpia by agreeing to his request, but then stabbing him dead after he has
given the order to use blanks. She does so, but too late discovers that Scarpia
chose to deceive her too. The firing squad does not use blanks; Cavaradossi
dies. Tosca commits suicide, and all three end up dead.
Though they did not put it this way, Tosca and Scarpia were playing a game, indeed the most famous game in all of game theory, an esoteric branch of mathematics that provides a strange bridge between biology and economics. The game has been central to one of the most exciting scientific discoveries of recent years: nothing less than an understanding of why people are nice to each other. Moreover, Tosca and Scarpia each played the game in the way that game theory predicts they should, despite the disastrous outcome for each. How can this be?
The game is known as the prisoner's dilemma, and it applies wherever there is a conflict between self-interest and the common good. Both Tosca and Scarpia would benefit if they stuck to their bargain: Tosca would save her lover's life and Scarpia would bed her. But as individuals each would benefit even more if he or she deceived the other into keeping his side of the bargain but did not keep his own: Tosca would save her lover and her virtue, whereas Scarpia would get lucky and be rid of his enemy.
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The
prisoner's dilemma presents us with a stark example of how to achieve
cooperation among egoists--cooperation that is not dependent on taboo, moral
constraint or ethical imperative. How
can individuals be led by self-interest to serve a greater good? The game is
called the prisoner's dilemma because the commonest anecdote to illustrate it
describes two prisoners each faced with the choice of giving evidence against
the other and so reducing his own sentence.
The dilemma arises because if neither defects on the other, the police
can convict them both only on a lesser charge, so both would be better off if
they stayed silent, but each is individually better off if he defects.
Why?
Forget prisoners and think of it as a simple mathematical game you play with
another player for points. If you
both cooperate ('stay silent') you each get three (this is called the 'reward');
if you both defect you each get one {the 'punishment'). But if one defects and
the other cooperates, the cooperator gets nothing (the 'sucker's pay-off') and
the defector gets five points (the 'temptation').
So, if your partner defects, you are better off defecting, too.
That way you get one point rather than none.
But if your partner cooperates, you are still better off defecting: you
get five instead of three. Whatever the other person does, you are better off
defecting. Yet, since he argues
the same way, the certain outcome is mutual defection: one point each, when you
could have had three each.
Do
not get misled by your morality. The
fact that you are both being noble in cooperating is entirely irrelevant to the
question. What we are seeking is the
logically 'best' action in a moral vacuum, not the 'right' thing to do.
And that is to defect. It is
rational to be selfish.
The
prisoner's dilemma, broadly defined, is as old as the hills; Hobbes certainly
understood it. So, too, did
Rousseau, who in passing described a rather sophisticated version sometimes
known as the co-ordination game in his famous but brief story of the stag hunt.
Picturing a group of primitive men out hunting, he said:
If it was a matter of hunting deer, everyone well realized that he must remain faithfully at his post; but if a hare happened to pass within reach |
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of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple and, having caught his own prey, he would have cared very little about having caused his companions to lose theirs. |
To
make it clear what Rousseau meant, suppose everybody in the tribe goes out to
hunt a stag. They do so by forming a
wide ring around the thicket in which the stag is lying, and walking inwards I
until the beast is finally forced to try to escape from the encircling cordon of
hunters, at which point, if all goes well, it is killed by the closest hunter.
But suppose one of the hunters encounters a hare.
He can catch the hare for sure, but only by leaving the circle.
That in turn leaves a gap through which the stag escapes. The hunter who
caught the hare is all right--he has meat-- but everybody else pays with an
empty belly the price of his selfishness. The
right decision for the individual is the wrong one for the group, so proving
what a hopeless project social cooperation is (said misanthropic Rousseau
bleakly).
A
modern version of the stag hunt is the game suggested by Douglas Hofstadter
called the 'wolf's dilemma'. Twenty
people sit, each in a cubicle, with their fingers on buttons. Each person will
get $1,000 after ten minutes, unless someone pushes his button, in which case
the person who pushed the button will get $100 and everybody else will get
nothing. If you are clever you do
not push the button and collect $1,000, but if you are very clever, you see that
there is a tiny chance that somebody will be stupid enough to push his or her
button, in which case you are better off pushing yours first, and if you are
very, very clever you see that the very clever people will deduce this and will
push their buttons, so you, too, had better push yours.
As in the prisoner's dilemma, true logic leads you into collective
disaster.
Old
as the idea may be, the prisoner's dilemma was first formalized as a game in
1950 by Merril Flood and Melvin Dresher of the RAND corporation in
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to
do something, but know it would be a great mistake if everybody did the same
thing, is likely to be a prisoner's dilemma. (The formal mathematical definition
of the prisoner's dilemma is wherever the temptation is greater than the reward,
which is greater than the punishment, which is greater than the sucker's
pay-off, though the game changes if the temptation is huge.)
If everybody could be trusted not to steal cars, cars need not be
locked and much time and expense could be saved in insurance premiums, security
devices and the like. We would all
be better off. But in such a
trusting world, an individual can make himself even better off by defecting from
the social contract and stealing a car. Likewise, all fishermen would be better
off if everybody exercised restraint and did not take too many fish, but if
everybody is taking as much as he can, the fisherman who shows restraint only
forfeits his share to somebody more selfish.
So we all pay the collective price of individualism.
Tropical
rain forests, bizarrely, are the products of prisoners' dilemmas. The trees that
grow in them spend the great majority of their energy growing upwards towards
the sky, rather than reproducing. If
they could come to a pact with their competitors to outlaw all tree trunks
and respect a maximum tree height of ten feet, every tree would be better off.
But they cannot.
To
reduce the complexity of life to a silly game is the kind of thing that gets
economists a bad name. But the point
is not to try to squeeze every real-life problem into a box called 'prisoner's
dilemma', but to create an idealized version of what happens when collective and
individual interests are in conflict. You
can then experiment with the ideal until you discover something surprising and
then return to the real world to see if it sheds light on what really
happens.
Exactly this has occurred with the prisoner's dilemma game (although some theorists have to be dragged kicking and screaming back to the real world). In the 1960s, mathematicians embarked on an almost manic search for an escape from the bleak lesson of the prisoner's dilemma--that defection is the only rational approach. They repeatedly claimed to have found one, most notably in 1966 when Nigel Howard rephrased the game in terms of the players'
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intentions, rather than their actions. But Howard's resolution of the paradox, like every other one suggested, proved only to be wishful thinking. Given the starting conditions of the game, cooperation is illogical.
This
conclusion was deeply disliked, not just because it seemed so immoral in its
implications, but because it seemed so at odds with the way real people behave.
Cooperation is a frequent feature of human society; trust is the very
foundation of social and economic life. Is
it irrational? Do we have to override our instincts to be nice to each other?
Does crime pay? Are people
honest only when it pays them to be so?
By
the
late 1970s, the prisoner's dilemma had come to represent all that was wrong with
the economist's obsession with self-interest.
If the game proved that the individually rational thing to do in such a
dilemma was to be selfish, then that only proved the inadequacy of the
assumption. Since people are not
invariably selfish, then they must not be motivated by self-interest, but by the
common good. Two hundred years of
classical economics, built on the assumption of self-interest, was therefore
barking up the wrong tree.
A
brief
digression on game theory: born, in 1944, in the fertile but inhuman brain of
the great Hungarian genius Johnny von Neumann, it is a branch of mathematics
that especially suits the needs of the 'dismal science' of economics. This is
because game theory is concerned with that province of the world where the right
thing to do depends on what other people do. The right way to add two and
two does not depend on the circumstances, but the decision whether to buy or
sell an investment does depend totally on the circumstances, and in particular
on what other people decide. Even in that case, though, there may be a foolproof
way to behave, a strategy that works whatever other people do.
To find it in a real situation, like making an investment decision, is
probably as close to impossible as makes no difference, but that does not mean
the perfect strategy does not exist. The
point of game theory is to find it in simplified versions of the world--to find
the universal prescription. This became known in the trade as the Nash
equilibrium, after the
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received
the Nobel Prize for it in 1994 on recovering from a long schizophrenic illness).
The
definition of a Nash equilibrium is when each player's strategy is an optimal
response to the strategies adopted by other players, and nobody has an incentive
to deviate from their chosen strategy.
Consider,
as an example, a game invented by Peter Hammerstein and Reinhard Selten.
There are two individuals, called Konrad and Niko; they have to share
money with each other. Konrad plays first and he must decide whether they will
share the money equally (fair) or unequally (unfair).
Niko plays second and he must decide how much money they will share: a
high or a low amount. If Konrad
plays unfair, he gets nine times as much as Niko.
If Niko plays high, each gets ten times as much as he would under the low
conditions. Konrad can demand nine
times as much as Niko and there is nothing Niko can do about it. If he plays
low, he punishes himself as well as Konrad.
So he cannot even plausibly threaten to punish Konrad by playing low.
The Nash equilibrium is for Konrad to play unfair and Niko to play high.
This is not the ideal outcome for Niko, but it is the best of a bad job.
Note
that the best outcome is not necessarily achieved at the Nash equilibrium.
Far from it. Often the Nash
equilibrium lies with two strategies that deliver one or both partners into
misery, yet neither can do any better by doing differently. The prisoner's
dilemma is just such a game. When
played a single time between naive partners, there is only one Nash equilibrium:
both partners defect.
Hawks
and Doves
Then
one experiment turned this conclusion on its head. For thirty years, it showed,
entirely the wrong lesson had been drawn from the prisoner's dilemma. Selfishness
was not the rational thing to do after all--so long as the game is played more
than once.
Ironically,
the resolution of this conundrum had been glimpsed at the very moment the game
was invented, then subsequently forgotten. Flood and Dresher discovered a rather
surprising phenomenon
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almost
straight away. When they asked two colleagues--Armen Alchian and John
Williams-to play the game 100 times for small sums of money, the guinea pigs
proved surprisingly keen to cooperate: on sixty
of the 100 trials both cooperated and captured the benefits of mutual aid.
Each admitted in notes made throughout the game that he was trying to be
nice to the other to lure him into being nice back--until the very end of the
game, when each saw the chance for a quick killing at the other's expense. When
the game was played repeatedly and indefinitely by a single pair of people,
niceness, not nastiness, seemed to prevail.
The
Alchian-Williams tournament was forgotten, yet whenever people were asked to
play the game, they proved remarkably likely to try cooperation, the logically
wrong tactic. This undue readiness
to cooperate was condescendingly put down to their irrationality and generally
inexplicable niceness. 'Evidently,'
wrote one pair of game theorists, 'the run-of-the-mill players are not
strategically sophisticated enough to have figured out that strategy D D [both
defect] is the only rationally defensible strategy.'
We were too dense to get it right.
In
the early 1970s, a biologist rediscovered the Alchian- Williams lesson. John
Maynard Smith, an engineer-geneticist, had never heard of the prisoner's
dilemma. But he saw that biology
could use game theory as profitably as economics.
He argued that, just as rational individuals should adopt strategies like
those predicted by game theory as the least worst in any circumstances, so
natural selection should design animals to behave instinctively with similar
strategies. In other words, the
decision to choose the Nash equilibrium in a game could be reached both by
conscious, rational deduction and by evolutionary history.
Selection, not the individual, can also decide.
Maynard Smith called an evolved instinct that met a Nash equilibrium an
'evolutionary stable strategy': no animal playing it would be worse off than an
animal playing a different strategy.
Maynard
Smith's first example was an attempt to shed light on why animals do not
generally fight to the death. He set
the game up as a contest between Hawk and Dove.
Hawk, which is roughly equivalent to 'defect' in the prisoner's dilemma,
easily beats Dove,
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but is bloodily wounded in a fight with another Hawk. Dove, which is equivalent to 'cooperate', reaps benefits when it meets another Dove, but cannot survive against Hawk. However, if the game is played over and over again, the softer qualities of Dove become more useful. In particular, Retaliator--a Dove that turns into a Hawk when it meets one--proves a successful strategy. We shall hear more of Retaliator shortly.
Maynard
Smith's games were ignored by economists, because they were in the world of
biology. But in the late 1970s
something rather disturbing began to happen. Computers started using their cold,
hard, rational brains to play the prisoner's dilemma, and they began to do
exactly the same thing as those foolish, naive human beings--to be irrationally
keen to cooperate. Alarm bells rang
throughout mathematics. In 1979, a
young political scientist, Robert Axelrod, set up a tournament to explore the
logic of cooperation. He asked
people to submit a computer program to play the game 200 times against each
other program submitted, against itself and against a random program.
At the end of this vast contest, each program would have scored a number
of points.
Fourteen
people submitted programs of varying complexity, and to general astonishment,
the 'nice' programs did well. None
of the eight best programs would initiate defection.
Moreover, it was the nicest of all--and the simplest of all--that won.
Anatol
Rapoport, a Canadian political scientist with an interest in nuclear
confrontation who was once a concert pianist and probably knew more about the
prisoner's dilemma than anybody alive, submitted a program called Tit-for-tat,
which simply began by cooperating and then did whatever the other guy did last
time. Tit-for-tat is in practice another name for Maynard Smith's Retaliator.
Alexrod held another tournament, asking people to try to beat Tit-for-tat. Sixty-two programs tried, and yet the one that succeeded was. . . Tit-for-tat itself! It again came out on top. As Axelrod explained in his book on the subject:
What accounts for Tit-for-tat's robust success is its combination of being nice, retaliatory, forgiving and clear. Its niceness prevents it from getting |
p.61
into unnecessary trouble. Its retaliation discourages the other side from persisting whenever defection is tried. Its forgiveness helps restore mutual cooperation. And its clarity makes it intelligible to the other player, thereby eliciting long-term cooperation. |
Axelrod's
next tournament pitted strategies against each other in a sort of
survival-of-the-fittest war, one of the first examples of what has since become
known as 'artificial life'. Natural
selection, the driving force of evolution, is easily simulated on a computer:
software creatures compete for space on the computer's screen in just the way
that real creatures breed and compete for space in the real world.
In Axelrod's version, the unsuccessful strategies gradually went to the
wall, leaving the most robust program in charge of the field.
This produced a fascinating series of events.
First, the nasty strategies thrived at the expense of nice, naive ones.
Only retaliators like Tit- for-tat kept pace with them.
But then, gradually, the nasty strategies ran out of easy victims and
instead kept meeting each other; they too began to dwindle in numbers.
Tit-for-tat now came to the fore and eventually once again, it stood in
sole command of the battlefield.
Axelrod
thought his results might be of interest to biologists, so he contacted a
colleague at the
p.
62
reciprocating
selfishly desired favours. Encouraged
by
Here,
suddenly, a decade later, in
They
were not long in coming. In 1983, the biologist Gerald Wilkinson returned to
Luckily,
however, for the bats, when they do get a meal they can usually drink more than
they immediately need and the surplus can be donated to another bat by
regurgitating some blood. This is a
generous act, and the bats find themselves in a prisoner's dilemma: bats who
feed each other are better off than bats that do not; however, bats that take
food but do not give it are best off and bats that give food but do not receive
it are worst off.
Since
the bats tend to roost in the same places, and can live for a long time--up to
eighteen years--they get to know each other as individuals, and they have the
opportunity to play the game repeatedly, just like Axelrod's computer programs.
They are not, inci-
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dentally,
very closely related on average to their neighbouring roost-mates, so nepotism
is not the explanation of their generosity.
Wilkinson
found that they seem to play Tit-for-tat. A bat that has donated blood in the
past will receive blood from the previous donee; a bat that has refused blood
will be refused blood in turn. Each
bat seems to be quite good at keeping score, and this may be the purpose
of
the social grooming in which the bats indulge.
The bats groom each other's fur, paying particular attention to the area
around the
stomach. It is hard for a bat that has a distended belly
after a good meal to disguise the fact from another bat which grooms it.
A bat
that
cheats is therefore soon detected. Reciprocity
rules the roost.
African
vervet monkeys are similarly reciprocal. When
played a tape recording of a call from one monkey requesting support in a
fight,
another monkey will respond much more readily if the caller has helped it in the
past.
But
if the two are closely related, the second monkey's response does not depend so
much on whether the first monkey has once helped it. Thus,
as theory predicts, Tit-for-tat is a mechanism for generating cooperation
between unrelated individuals. Babies
take their mother's beneficence for granted and do not have to buy it with acts
of kindness. Brothers and sisters do
not feel the need to reciprocate every kind act.
But unrelated individuals are acutely aware of social debts.
The
principal condition required for Tit-for-tat to work is a stable, repetitive
relationship. The more casual and
opportunistic the encounters between a pair of individuals, the less likely it
is that Tit-for-tat will succeed in building cooperation.
Trivers noticed that support for this idea can be found in an unusual
feature of coral reefs: cleaning stations. These are specific locations on the
reef where local large fish, including predators, know they can come and will be
'cleaned' of parasites by smaller fish and shrimps.
This
form of cleaning is a vitally important part of being a tropical fish. More than
forty-five species of fish and at least six of shrimp offer cleaning services on
coral reefs, some of them relying on it as their sole source of food, and most
of them exhibiting distinctive colours and activities that mark them out to
potential clients as cleaners. Fish of all kinds visit them to be cleaned, often
coming in
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from
the open ocean, or out from hiding places under the reef, and some specially
change their colour to indicate a need for a clean; it seems to be a
particularly valuable service for large fish.
Many fish spend as much time being cleaned as feeding, and return several
times a day to be cleaned, especially if wounded or sick.
If the cleaners are removed from a reef there is an immediate effect: the
number of fish declines, and the number showing sores and infections increases
rapidly as the parasites spread.
The
smaller fish get food and the larger fish get cleaned: mutual benefit results.
But the cleaners are often the same size and shape as the prey of the
fish they clean, yet the cleaners dart in and out of the mouths of their
clients, swim through their gills and generally dice with death.
Not only are the cleaners unharmed, but the clients give careful and well
understood signals when they have had enough and are about to move on; the
cleaners react to these signals by leaving straight away.
So strong are the instincts that govern cleaning behaviour that in one
case cited by Trivers, a large grouper, reared for six years in an aquarium tank
until he was four feet long, and accustomed to snapping up any fish thrown into
his tank, reacted to the first cleaner he met by opening his mouth and gills to
invite the cleaner in, even though he had no parasites at all.
The
puzzle is why the clients do not have their cake and eat it:
accept the cleaning services, but round off the session by eating the
cleaner. This would be equivalent to defecting in the prisoner's dilemma.
And it is prevented for exactly the same reason as defection is rare.
The answer is roughly the same as an amoral New Yorker would probably
give when asked why he bothers to pay his illegal-immigrant cleaning lady rather
than just fire her and get another one next week: because good cleaners are hard
to find. The client fish do not
spare their cleaners out of a general sense of duty to future clients, but
because a good cleaner is more valuable to them as a future cleaner than as a
present meal. This
is so only because the same cleaner can be found in the same spot on the same
reef day after day for years on end. The
permanence and duration of the relationship is vital to the equation. One-shot
encounters encourage
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defection;
frequent repetition encourages cooperation.
There are no cleaning stations in the nomadic life of the open ocean.
Another
example Axelrod explored was the Western Front in the First World War.
Because of the stalemate that developed, the war turned into one long
battle over the same piece of ground, so that the encounters between any two
units were repeated again and again. This
repetition, like the repetition of games in the prisoner's dilemma, changed the
sensible tactic from hostility to cooperation, and indeed the Western Front was
'plagued' by unofficial truces between Allied and German units that had been
facing each other for some time. Elaborate
systems of communication developed
to
agree terms, apologize for accidental infractions and ensure relative peace--all
without the knowledge of the high commands on each side. The
truces were policed by simple revenge. Raids and artillery barrages were used to
punish the other side for defection, and these sometimes escalated out of
control in just the way that blood feuds do. Thus, the situation bore a strong
resemblance to Tit-for-tat: it produced mutual cooperation, but responded to
defection with defection. The simple and effective 'remedy', put into practice
by both sides' generals when the truces were discovered, was to move units about
frequently, so that no regiment was opposite any other for long enough to build
up a relationship of mutual cooperation.
However,
there is a dark side to Tit-for-tat, as mention of the First World War reminds
us. If two
Tit-for-tat players meet each other and get off on the right foot, they
cooperate indefinitely. But if one of them accidentally or unthinkingly defects,
then a continuous series of mutual recriminations begins from which there is no
escape. This, after all, is the
meaning of the phrase 'tit-for-tat killing' in places where people are or have
been addicted to factional feuding and revenge, such as Sicily, the Scottish
borders in the sixteenth century, ancient Greece and modern Amazonia.
Tit-for-tat, as we shall see, is no universal panacea.
But
the lesson for human beings is that our frequent use of reciprocity in society
may be an inevitable part of our natures: an instinct. We do not need to reason
out way to the conclusion that 'one good
p.66
turn
deserves another', nor do we need to be taught it against our better judgements.
It simply develops within us as we mature, an ineradicable predisposition, to be
nurtured by teaching or not as the case may be.
And why? Because natural selection has chosen it to enable us to get more
from social living.
Chapter
Four
Telling
Hawks From Doves
In
which developing a good reputation pays
p.69
For
their size, vampire bats have very big brains. The reason is that the neocortex--the
clever bit at the front of the brain--is disproportionately big compared to the
routine bits towards the rear. Vampire
bats have by far the largest neocortexes of all bats.
It is no accident that they have more complex social relationships than
most bats, including, as we have seen, bonds of reciprocity between unrelated
neighbours in a group. To
play the reciprocity game, they need to recognize each other, remember who
repaid a favour and who did not, and bear the debt or the grudge accordingly.
Throughout the two cleverest families of land-dwelling mammals, the primates and
the carnivores, there is a tight correlation between brain size and social
group. The bigger the society in
which the individual lives, the bigger its neocortex relative to the rest of the
brain. To
thrive in a complex society, you need a big brain.
To acquire a big brain, you need to live in a complex society.
Whichever way the logic goes, the correlation is compelling.
Indeed,
so tight is the correlation that you can use it to predict the natural group
size of a species whose group size is unknown. Human beings, this logic
suggests, live in societies 150 strong. Although
many towns and cities are bigger than this, the number is in fact about right.
It is roughly the number of people in a typical hunter-gatherer band, the
number in a typical religious commune, the number in the average address book,
the number in an army company, the maximum number employers prefer in an easily
run factory. It is, in short, the number of people we each know well.
Reciprocity
only works if people recognize each other.
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You
cannot
pay back a favour, or hold a grudge, if you do not know how to find and identify
your benefactor or enemy. Moreover,
there is one vital ingredient of reciprocity that our discussion of game theory
has so far omitted: reputation. In a
society of individuals that you recognize and know well, you need never play the
prisoner's dilemma blindly. You can
pick and choose your partners. You
can pick those you know have cooperated in the past, you can pick those whom
others have told you can be trusted, and you can pick those who signal that they
will cooperate. You can
discriminate.
Large,
cosmopolitan cities are characterized by ruder people and more casual insult and
violence than small towns or rural areas. Nobody
would dream of driving in their home suburb or village as they do in
In
the conditions in which human beings evolved, in small tribes where to meet a
stranger must have been an extremely rare event, this sense of reciprocal
obligation must have been palpable--it still is among rural people of all kinds.
Perhaps
Tit-for-tat is at the root of the human social instinct; perhaps it explains
why, of all mammals, the human being has come closest to matching the naked mole
rat in its social instincts.
The
Hunting of the Snark
After
Robert Axelrod's tournaments, there was a minor backlash against Tit-for-tat in
game theory. Economists and zoologists alike began to crowd in with awkward
objections.
p.71
The
main
problem that zoologists have with Tit-for-tat is that there are so few good
examples of it from nature. Apart
from Wilkinson's vampire bats, Trivers's reef cleaning stations and a handful of
examples from dolphins, monkeys and apes, Tit-for-tat just is not practised.
These few examples are a meagre return on the effort that went into looking for
Tit-for-tat in the 1980s. To some zoologists the conclusion is stark: animals
ought to play Tit-for-tat, but they don't.
A
good example is lions. Lionesses
live in tight-knit prides, each pride defending its territory against rival
prides (male lions just attach themselves to prides for the sex, and do little
of the work, either catching food or defending territory--unless it be from
other males). Lionesses
advertise their territorial ownership by roaring, so it is quite easy to fool
them into thinking they face a serious invasion by playing tape-recorded roars
in their territories. This Robert
Heinsohn and Craig Packer did to some Tanzanian lions and watched their
reaction.
The
lionesses usually walk towards the sound to investigate, some rather
enthusiastically, others a little reluctantly.
This is fertile territory for Tit-for-tat. A brave lioness, who leads the
approach to the 'intruder', should expect a reciprocal favour from a laggard,
who hangs back: next time the laggard should lead, and risk danger.
But Heinsohn and Packer found no such pattern. Leaders recognize laggards
and keep looking back at them as if resentfully, but they usually lead the next
time, too. Laggards
are laggards.
We
suggest that female lions may be classified according to four discrete
strategies: 'unconditional cooperators' who always lead the response,
'unconditional laggards' who always lag behind, 'conditional cooperators' who
lag least when they are most needed, and 'conditional laggards' who lag farthest
when they are most needed.)
There
is absolutely no sign of punishment for the laggards, or reciprocity.
The leaders just have to accept that their courage goes unappreciated.
The lionesses do not play Tit-for-tat.
The
fact that other animals do not often play Tit-for-tat does not prove that human
beings do not build their societies upon reciprocity.
p.72
As
we shall see in the next few chapters, the evidence that human society is
riddled with reciprocal obligations is great and growing greater all the time.
Like language and opposable thumbs, reciprocity might be one of those things
that we have evolved for our own use, but that few other animals have found the
use or the mental capacity for.
Kropotkin may have been wrong, in other words, to expect mutual aid in insects
just because it is present in people. Nonetheless,
the zoologists have a point. The simple idea of Tit-for-tat seems better suited
to the simplified world of computer tournaments than the mess that is real life.
Economists
had a different problem with Tit-for-tat. Axelrod's discoveries, published in a
series of papers and later in a book called The Evolution of Co-operation, caught
the popular imagination and were widely publicized in the press. This fact alone
would have earned them contempt from envious game theorists, and sure enough the
sniping soon began.
Juan
Carlos Martinez-Coli and Jack Hirshleifer put it bluntly: 'A rather astonishing
claim has come to be widely accepted: to wit that the simple reciprocity
behaviour known as Tit-for-tat is a best strategy not only in the particular
environment modeled by Axelrod's simulations but quite generally.'
They
argued that one could just as easily design the conditions of a tournament in
which Tit-for-tat would not do well, and, more worryingly, it seemed to be
impossible to simulate a world where both nasty and nice strategies
cohabited--yet that is the world we live in.
Among
the harshest critics has been Ken Binmore. He
argues that it is vital to notice that, even in Axelrod's simulations,
Tit-for-tat never wins a single game against a 'nastier' strategy: therefore, it
is singularly bad advice to play Tit-for-tat if you enter a single game, rather
than a series of games. You're just
a sucker if you do. Axelrod,
remember, added the scores obtained in matches between many
p.73
different
strategies. Tit-for-tat won by accumulating many high-scoring draws and losses,
not by winning bouts.
Binmore
believes that the very fact that we find Tit-for-tat such a natural idea--'we
all know deep down inside that it is reciprocity that keeps society
going'--makes us uncritically keen to accept a mathematical rationalization of
the notion. He adds: 'One must be
very cautious indeed before allowing oneself to be persuaded to accept general
conclusions extrapolated from computer simulations.
Much
of this criticism misses the point. Axelrod should no more be criticized for
failing to capture everything that happens in the world than Newton should be
for failing to explain politics in terms of gravity.
Everybody thought the prisoner's dilemma taught a bleak lesson, not only that it
was rational to defect but also that it was stupid of people not to realize
this. Yet Axelrod
discovered that, in his words, 'the shadow of the future' alters this
completely. A simple, nice strategy won his tournaments again and again. Even if
his conditions later prove unrealistic, even if life is not precisely such a
tournament, Axelrod's work has thoroughly demolished the working assumption of
all those who had studied the subject before: that the only rational
thing to do in a prisoner's dilemma is to be nasty. Nice guys can finish first.
As
for the argument that Tit-for-tat wins by losing in high-scoring games, that is
the whole point. Tit-for-tat loses
or draws each battle but wins the war, by ensuring that most of its contests are
high-scoring affairs, so it brings home the most points.
Tit-for-tat does not envy or wish to 'beat' its opponent.
Life, it believes, is not a zero-sum game: my success need not be at your
expense; two can 'win' at once. Tit-for-tat
treats each game as a deal struck between the participants, not a match between
them.
Some
of the highland people in central New Guinea, who live in a network of
dangerous, unstable, but reciprocal alliances and feuds between tribes, have
recently taken up football but, finding it a little too much for the blood
pressure to lose a game, they have adjusted the rules.
The game simply continues until each side has scored a certain number of
goals. A good time is had by all,
but there is no
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loser
and every goal scorer can count themselves a winner.
It is not a zero-sum game.
'Don't
you see?' remonstrated the referee, a newly arrived priest, after one such drawn
game. 'The object of the game is to
try to beat the other team. Someone
has to win!' The captains of the
rival teams replied, patiently, 'No, Father. That's not the way of things.
Not here in Asmat. If someone
wins then someone else has to lose--and that would never do.
This
is bizarre only because it is an idea we find so instinctively hard to grasp, at
least in the context of games (I have my doubts about the joys of
Imagine
a football tournament slightly different from the
However,
in one important respect, Binmore and the other critics were right.
Axelrod had been too hasty in concluding that Tit-for-tat itself is
'evolutionarily stable'--meaning that a population playing Tit-for-tat is immune
to invasion by any other strategy. This
conclusion was undermined by further computer-simulated tournaments, like
Axelrod's third one, in which Rob Boyd and Jeffrey Lorberbaum showed that it was
easy to design tournaments that Tit-for-tat does not win.
p.75
In
these tournaments, to recapitulate, a random mix of strategies battle against
each other for control of a finite space, by breeding at the rate defined by
their points in the last game: 5, 3, I or 0.
In these conditions, nasty strategies, such as �always defect�, do
well at first, exploiting the naive cooperative strategies and crowding them
out. But soon they get sluggish and
feeble, because they only ever meet each other, and only ever get I point.
Now is when Tit-for- tat comes into its own.
Playing against �always
defect�, it soon defects to deprive the other of more than one 5-point
temptation; but, playing against itself, it cooperates and reaps 3 points.
Therefore, so long as one Tit-for-tat can find a few others and form even
a small cooperative cluster, they can thrive and drive �always defect�
extinct.
But
it is now that Tit-for-tat's weaknesses emerge.
For example, Tit-for-tat is vulnerable to mistakes.
Remember that it cooperates until it meets a defection, which it then
punishes. When two Tit-for-tat
players meet they cooperate happily, but if one starts to defect, purely by
random mistake, then the other retaliates and before long both are locked in a
miserably unprofitable round of mutual defections.
To take an all-too-real example, when an IRA gunman in
Because
of such weaknesses, it was apparent that Tit-for-tat's success in the Axelrod
tournaments was largely a function of their form. The tournaments just happened
not to show up these weaknesses. In a world where mistakes are made, Tit-for-tat
is a second-rate strategy, and all sorts of other strategies prove better. The
clear conclusions that Axelrod had drawn became clouded as ever more rococo
elaborations of new strategies were invented.
The
scene now shifts to
Nowak
designed a different kind of tournament, one in which nothing was certain, and
everything was statistically driven. Strategies
made random mistakes with certain probabilities, or switched between tactics in
the same probability-driven manner. But
the system could 'learn' or evolve by keeping improvements and dropping
unsuccessful tactics. Even the
probabilities with which they did things were open to gradual evolutionary
change. This new realism proved
remarkably helpful, stripping away all the rococo complications.
Instead of several strategies equally capable of winning the game, one
clearly came out on top. It was not
Tit-for-tat but a very near relation called Generous-Tit-for-tat (which I will
call Generous, for short).
Generous
occasionally forgives single mistakes. That
is, about one-third of the time it magnanimously overlooks a single defection.
To forgive all single defections--a strategy known as
Tit-for-two-tats--is merely to invite exploitation.
But to do so randomly with a probability of about a third is remarkably
effective at breaking cycles of mutual recrimination while still remaining
immune to exploitation by defectors. Generous will spread at the expense of
Tit-for-tat in a computer population of pure Tit-for-tat players that are making
occasional mistakes. So, ironically,
Tit-for-tat merely paves the way for a nicer strategy than itself.
It is John the Baptist, not the Messiah.
But
neither is Generous the Messiah. It
is so generous that it allows even nicer, more naive strategies to spread. For
example, the simple
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strategy �always cooperate� can thrive among Generous players, though it does not actually defeat them; it can creep back from the dead. But �always cooperate� is a fatally generous strategy and is easily invaded by �always defect�, the nastiest strategy of all. Among Generous players, �Always defect� gets nowhere; but when some start playing �always cooperate�, it strikes. So, far from ending up with a happy world of reciprocity, Tit-for-tat ushers in Generous, which can usher in �Always cooperate�, which can unleash perpetual defection, which is back where we started from. One of Axelrod's conclusions was wrong: there is no stable conclusion to the game.
As
the summer of 1992 began, Sigmund and Nowak were depressed by their conclusion
that there is no stable solution to the prisoner's dilemma game.
It is the sort of untidy decision game theorists dislike.
But, as luck would have it, Sigmund's wife, a historian, was due to spend
the summer in Schloss Rosenburg, a fairy-tale castle in the Waldviertel of lower
They
went back to the beginning and entered into the lists of their tournaments all
sorts of strategies that had been rejected before, trying to find one that not
only won, but could remain stable after winning the tournament. They tried
giving their playing automata a slightly better memory. Instead of just reacting
to the partner's last play, as Tit-for-tat does, the new strategies remembered
their own last play as well and acted accordingly.
One day, quite suddenly, as the eagles dived past the window, inspiration
struck. An old strategy first tried
by--who else?--Anatol Rapoport, suddenly kept coming out on top.
Rapoport
had dismissed the strategy as hopeless, calling it Simpleton. But that
was because he had pitted it against �always defect�, against which it was
indeed naive. Nowak and Sigmund
entered it into a world dominated by Tit-for-tat and it
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not
only defeated the old pro, but proved invincible thereafter.
So, although Simpleton cannot beat �always defect�, it can steal the
show once Tit-for-tat has extinguished �always
defect�. Once again, Tit-for-tat plays John the Baptist.
Simpleton's
other name is Pavlov, though some say this is even more misleading--it is the
opposite of reflexive. Nowak admits that he should call it by the cumbersome but
accurate name of Win-stay/Lose-shift, but he cannot bring himself to do so, so
Pavlov it remains.
Pavlov is like a rather simplistic roulette gambler.
If he wins on red, he sticks to red next time; if he loses, he tries
black next time. For win, read 3 or
5 (reward and temptation); for lose, read I or 0 (punishment and sucker's
pay-off). This
principle--that you don't mend your behaviour unless it is broken--underlies a
lot of everyday activities, including dog training and child-rearing. We bring
up our children on the assumption that they will continue doing things that are
rewarded and stop doing things that are punished.
Pavlov
is nice, like Tit-for-tat, in that it establishes cooperation, reciprocating in
that it tends to repay its partners in kind, and forgiving, like Generous, in
that it punishes mistakes but then returns to cooperating. Yet it has a
vindictive streak that enables it to exploit naive cooperators like �always
cooperate�. If it comes up against
a sucker, it keeps on defecting. Thus
it creates a cooperative world, but does not allow that world to decay into a
too-trusting Utopia where free-riders can flourish.
Yet
Pavlov's weakness was well known. As Rapoport had discovered, it is usually
helpless, in the face of �always defect�, the nasty strategy.
It keeps shifting to cooperation and getting the sucker's pay-off--hence
its original name of Simpleton.
So
Pavlov cannot spread until Tit-for-tat has done its job and cleared out the bad
guys. Nowak and Sigmund, however,
discovered that Pavlov only shows this flaw in a deterministic game--one in
which all the strategies are defined in advance.
In their more realistic world of probability and learning, where each
strategy rolled a die to decide what to do next, something very different
happened. Pavlov quickly adjusted
its probabilities to the point where its supremacy could not be challenged by
�always defect�. It was truly
evolutionarily stable.
p.79
Do
animals or people use Pavlov? Until
Nowak and Sigmund published their idea, one of the neatest examples of
Tit-for-tat from animals was an experiment by Manfred Milinski using fish called
sticklebacks. Sticklebacks
and minnows are eaten by pike, and they react to the presence of a pike by
leaving the school in a small scouting party and approaching it cautiously to
assess the danger it poses. This
apparently foolish courage must have some reward; naturalists think it gives the
prey some valuable information. If,
for example, they conclude that the pike is not hungry or has just fed, they can
return to feeding themselves.
When
two sticklebacks inspect a predator together, they move forward in a series of
short spurts, one fish taking the initiative and risk each time.
If the pike moves, both dash back again.
Milinski argued that this was a series of small prisoner's dilemmas, each
fish having to offer the 'cooperative' gesture of the next move forward, or take
the 'defector's' option of letting the other fish go ahead alone.
By an ingenious use of mirrors, Milinski presented each fish with an,
apparent companion (in fact its own reflection) that either kept up with it or
lagged further and further behind as it got nearer the pike. Milinski at first
interpreted his results in terms of Tit-for-tat: the trial fish was bolder with
a cooperator than a defector. But, on hearing about Pavlov, he recalled that his
fish would seem to switch back and forth between cooperation and defection when
presented with a consistently defecting companion that had previously once
cooperated--like Pavlov but unlike Tit-for-tat.
It
may seem absurd to look at fish, expecting to find sophisticated game theorists,
but there is, in fact, no requirement in the theory that the fish understand
what it is doing. Reciprocity can
evolve in an entirely unconscious automaton, provided it interacts repeatedly
with other automata in a situation that resembles a prisoner's dilemma--as the
computer simulations prove. Working out the strategy is the job not of the fish
itself, but of evolution, which can then program it into the fish.
p.80
Pavlov
is not the end of the story. Since
Nowak has moved to
The
significance of this is not to raise Firm-but-fair into a new god, but to notice
that making the game asynchronous makes guarded generosity even more rewarding.
This accords with common sense. If
you have to act before your partner and vice versa, it pays to try to elicit
cooperation by being nice. You do not, in other words, greet strangers with a
scowl lest they form a bad opinion of you; you greet them with a smile.
Reciprocity
has a hard enough time producing cooperation even within a pair: the pair must
be able to police their contract by being sure of encountering and recognizing
each other again. How
much harder is it among three individuals or more?
The larger the group, the more inaccessible are the benefits of
cooperation and the greater
p.81
the
obstacles that stand in the way. Indeed,
Rob Boyd, a theorist, has argued that not only Tit-for-tat but any reciprocal
strategy is simply inadequate to the task of explaining cooperation in large
groups. The reason is that a
successful strategy in a large group must be highly intolerant of even rare
defection, or else free-riders--individuals who defect and do not
reciprocate--will rapidly spread at the expense of better citizens.
But the very features that make a strategy intolerant of rare defection
are those that make it hard for reciprocators to get together when rare in the
first place.
Boyd
himself provides one answer. Reciprocal cooperation might evolve, he suggests,
if there is a mechanism to punish not just defectors, but also those who fail to
punish defectors. Boyd calls this a 'moralistic' strategy, and it can cause any
individually costly behaviour, not just cooperation, to spread, whether it
causes group benefit or not. This is actually a rather spooky and authoritarian
message. Whereas Tit-for-tat suggested the spread of nice behaviour among
selfish egoists without any authority to tell them to be nice, in Boyd's
moralism we glimpse the power that a fascist or a cult leader can wield.
There
is another and potentially more powerful answer to the problem of free-riders in
large groups: the power of social ostracism.
If people can recognize defectors, they can simply refuse to play games
with them. That effectively deprives the defectors of Temptation (5), Reward (3)
and even Punishment (1). They do not get a chance to accumulate any points at
all.
Philip
Kitcher, a philosopher, designed an �optional prisoner's dilemma� game to
explore the power of ostracism. He
populated a computer with four kinds of strategist: discriminating altruists,
who play only with those who have never defected on them before; willing
defectors, who always try defecting; solitaires, who always opt out of any
encounter; and selective defectors who are prepared to play with those who have
never defected before - but then, treacherously, defect on them.
Discriminating
altruists (DAs) invading a population of solitaires soon prevail, because they
find each other and reap the Reward. But
surprisingly, selective defectors cannot then invade a population of
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DAs,
whereas DAs can invade one of selective defectors. In
other words, discriminating altruism, which is just as �nice� as
Tit-for-tat, can reinvade anti-social populations. It
is no more stable than Tit-for- tat, because of a similar vulnerability to a
gradual take-over by undiscriminating cooperators. But
its success hints at the power of ostracism to help in solving prisoners'
dilemmas.
Kitcher's
programs relied entirely on the past behaviour of partners to judge whether they
could be trusted. But discriminating
between potential altruists need not be so retrospective. It
might be possible to recognize and avoid potential defectors in advance.
Robert Frank, an economist, set up
an experiment to find out. He put a
group of strangers in a room together for just half an hour, and asked them each
to predict privately which of their fellow subjects would cooperate and which
would defect in a single prisoner's dilemma game. They
proved substantially better than chance at doing so. They
could tell, even after just thirty minutes' acquaintance, enough about somebody
to predict his cooperativeness.
Frank
does not claim that this is too surprising. We spend a good deal of our lives
assessing the trustworthiness of others, and we make instant judgements with
some confidence. He poses a thought experiment for those unconvinced. �Among
those you know (but have never observed with respect to pesticide disposal), can
you think of anyone who would drive, say, forty-five minutes to dispose of a
highly toxic pesticide properly? If
yes, then you accept the premise that people can predict cooperative
predispositions.�
Can fish be trusted?
Now,
suddenly, there is a new and powerful reason to be nice: to persuade people to
play with you. The reward of cooperation, and the temptation
of defection, are forbidden to those who do not demonstrate trustworthiness
and build a reputation for it. Cooperators can seek out cooperators.
Of
course, for such a system to work, individuals must learn to recognize each
other, which is not an easy feat.
I have no idea
p.
83
whether
a herring in a shoal of 10,000 fish or an ant in a colony of 10,000 insects,
ever says to itself: 'There's old Fred again..' But I feel quite safe in
assuming that it does not. On
the other hand I feel equally secure in asserting that a vervet monkey probably
knows by sound and sight every other member of its troop, because the
primatologists Dorothy Cheney and Robert Seyfarth have proved as much.
Therefore, a monkey has the necessary attributes for reciprocating cooperation,
but a herring does not.
However,
I may be maligning fish. Manfred Milinksi and Lee Alan Dugatkin have discovered
a remarkably clear pattern of ostracism in stickleback fish when they risk their
lives to inspect predators. A fish will tolerate more defection on the part of
another fish that has continuously cooperated in the past than one that has not
cooperated. And
sticklebacks tend to pick the same partners to accompany them on
predator-inspection visits each time--choosing partners who are consistently
good cooperators. In other words,
not only are the sticklebacks quite capable of recognizing individuals, but they
seem capable of keeping individual scores--remembering which fish can be
'trusted'.
This
is a puzzling discovery, in the light of how rare reciprocal cooperation is, in
the animal kingdom. Compared to nepotism, which accounts for the cooperation of
ants and every creature that cares for its young, reciprocity has proved to be
scarce. This, presumably, is due to
the fact that reciprocity requires not only repetitive interactions, but also
the ability to recognize other individuals and keep score. Only
the higher mammals--apes, dolphins, elephants and a few others--are thought to
possess sufficient brain power to be so discriminating for more than a handful
of individuals. Now we know that sticklebacks can also keep score, at least for
one or two 'friends', this assumption may have to be relaxed.
Whatever
the capability of sticklebacks, there is no doubt that human beings, with their
astonishing ability to recall the features of even the most casual acquaintance
and their long lives and long memories, are equipped to play optional prisoner's
dilemma games with far greater aplomb than any other species. Of all the species
on the planet most likely to satisfy the criteria of prisoner's dilemma
p.84
tournaments--the
ability to 'meet repeatedly, recognize each other and remember the outcomes of
past encounters', as Nowak has put it--human beings are the most obvious.
Indeed, it might be what is special about us: we are uniquely good at reciprocal
altruism.
Think
about it: reciprocity hangs, like a sword of Oamocles, over every human head. He's
only asking me to his party so I'll give his book a good review. They've
been to dinner twice and never asked us back once. After
all I did for him, how could he do that to me? If
you do this for me, I promise I'll make it up later. What
did I do to deserve that? You owe it
to me. Obligation; debt; favour;
bargain; contract; exchange; deal. . . Our
language and our lives are permeated with ideas of reciprocity. In
no sphere is this more true than in our attitude to food.