The Origins of Virtue

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.

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

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 California and first rephrased as an anecdote about prisoners by Albert Tucker of Princeton University a few months later. As Flood and Dresher realized, prisoners' dilemmas are all around us. Broadly speaking any situation in which you are tempted

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'

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 Princeton mathematician John Nash (who worked out the theory in 1951, and

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.

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

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,

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

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.

Bat blood brothers

Axelrod thought his results might be of interest to biologists, so he contacted a colleague at the University of Michigan , none other than William Hamilton, who was immediately struck by a coincidence. More than ten years before, a young biology graduate student at Harvard named Robert Trivers had shown Hamilton an essay he had written. Trivers assumed that animals and people are usually driven by self-interest yet observed that they frequently cooperate. He argued that one reason self-interested individuals might cooperate was because of 'reciprocity': essentially, you scratch my back, and I'll scratch yours. A favour done by one animal could be repaid by a reverse favour later, to the advantage of both, so long as the cost of doing the favour was smaller than the benefit of receiving it. Therefore, far from being altruistic, social animals might be merely

reciprocating selfishly desired favours. Encouraged by Hamilton , Trivers eventually published a paper setting out the argument for reciprocal altruism in the animal kingdom and citing some likely examples. Indeed, Trivers went as far as to describe the repeated prisoner's dilemma as a means of testing his idea and predicting that the longer a pair of individuals interacted, the greater the chance of cooperation. He virtually predicted Tit-for-tat.

Here, suddenly, a decade later, in Hamilton 's hands, was mathematical proof that Trivers's idea had real power. Axelrod and Hamilton published a joint paper called 'The evolution of cooperation', to draw biologists' attention to Tit-for-tat. The result was an explosion of interest and a search for real examples among animals.

They were not long in coming. In 1983, the biologist Gerald Wilkinson returned to California from Costa Rica with a slightly grisly story of cooperation. Wilkinson had studied vampire bats, which spend the day in hollow trees and the night searching for large animals whose blood they can quietly sip from small cuts surreptitiously made in their skin. It is a precarious life, because a bat occasionally returns hungry, having either failed to find an animal or been prevented from drinking its fill from the wound. For old bats this happens only about one night in ten; but for young bats one night in three is unsuccessful, and two abortive nights in a row are not therefore uncommon. After as little as sixty hours without a blood meal, the bat is in danger of starving to death.

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-

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

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

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

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

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.

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.

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 Manhattan or central Paris--shaking fists at other drivers, hooting the horn, generally making clear their impatience. It is also widely acknowledged why this is the case. Big cities are anonymous places. You can be as rude as you like to strangers in New York, Paris or London and run only a minuscule risk of meeting the same people again (especially if you are in a car). What restrains you in your home suburb or village is the acute awareness of reciprocity. If you are rude to somebody, there is a good chance they will be in a position to be rude to you in turn. If you are nice to people, there is a good chance your consideration will be returned.

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.

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.

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.

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.

Tit-for-tat's Achilles' heel

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

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

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 New Guinea football). Take the case of trade. It is axiomatic among economists that the gains from trade are mutual: if two countries increase their trade, both are better off. Yet this is not the way the man in the street, let alone his demagogue representative, sees it. To them, trade is a competitive matter: exports good, imports bad.

Imagine a football tournament slightly different from the New Guinea case. In this competition the winner of the league is the team to score the most goals, not the one that wins most games. Now imagine that some teams decide to play normal football, letting in as few goals as possible and scoring as many as possible. Other teams try a different strategy. They let the other team score a goal, then try to score themselves. If allowed, they return the favour; and so on. You can quickly see which teams will do best: the ones that are playing Tit-for-tat. Football has thus been changed from a zero-sum game to a non-zero-sum game. What Axelrod achieved was precisely to turn the prisoner's dilemma from a zero-sum game into a non-zero-sum game. Life is very rarely a zero-sum game.

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.

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 Northern Ireland, aiming at a British soldier, kills an innocent Protestant bystander, the mistake can spark a revenge murder of a randomly selected Catholic by a loyalist gunman, which in turn is avenged, and so on ad infinitum. Such a series of deaths in Northern Ireland was known for many years as tit-for-tat killing.

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.

p.76

Enter Pavlov

The scene now shifts to Vienna, where Karl Sigmund, an ingenious mathematician with a playful cast of mind, was giving a seminar on game theory to a group of students one day in the late 1980s. One of the students in the audience, Martin Nowak, decided there and then to abandon his own studies of chemistry and become a game theorist. Sigmund, impressed by Nowak's determination, set him the task of solving the thicket of complication that had entrapped the prisoner's dilemma in the wake of Tit-for-tat. Find me the perfect strategy in a realistic world, said Sigmund.

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

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 Austria, as the guest of a Graf whose ancestry she was studying. Sigmund asked Nowak along and they brought a pair of laptop computers to play prisoner's dilemma tournaments. The castle is used as a falconry school and, by day, the two mathematicians found themselves distracted every two hours by the thousand-foot dives of imperial eagles practising their technique over the castle courtyard. It was a suitably medieval setting for the jousting matches they organized inside their computers.

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

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.

The fish that play chicken

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.

Pavlov is not the end of the story. Since Nowak has moved to Oxford it became inevitable that somebody at Cambridge had to take up the challenge of surpassing Pavlov. That somebody was Marcus Frean, who tried a new trick of playing the game in a more realistic fashion, in which the two players do not have to move simultaneously. Vampire bats do not do each other favours at the same moment. They take turns-- there would be no point in simply swapping food for fun. Frean ran a tournament of this ‘alternating prisoner's dilemma’ inside his computer and, sure enough, there evolved a strategy that defeated Pavlov. Frean calls it Firm-but-fair. Like Pavlov it cooperates with cooperators, returns to cooperating after a mutual defection and punishes a sucker by further defection. But unlike Pavlov it continues to cooperate after being the sucker in the previous round. It is, therefore, slightly nicer.

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.

The First Moralizers

Yet a more formidable problem looms. The prisoner's dilemma is a two-person game. Cooperation can, it seems, evolve spontaneously if a pair of individuals plays the game together indefinitely. Or, to put it more accurately, in a world where you only ever meet your immediate neighbour, it pays to be nice to him. But the world is not like that.

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

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

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.’

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

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

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.