Genius by James Gleick

Dawkins, Richard (1989), The Selfish Genes, Oxford University Press, New York: NY. ISBN 0-19-286092-5

The Selfish Gene - Richard Dawkins

There are two reasons I had for reproducing this chapter here. First is that the concepts and ideas presented in this chapter are pretty cool. Not usually given to colloquial expression in my writing, let me elaborate. Dawkins takes a seminal piece of work in game theory by Robert Axelrod and shows how it relates to evolution. The Axelrod work is an amazing and clever bit of science and, at the time, showed a very interesting benefit of computer modeling. The original paper is a bit dry and Dawkins does a very nice job of describing and elaborating on the methods and results of the work. To be fair, both Dawkins and Axelrod simply place the original problem of the Prisoner's Dilemma (created at the Rand Corporation in 1950 by Merrill Flood and Melvin Dresher as part of an effort to study strategies in intercontinental nuclear war) in the context of fitness and evolution. The Prisoner's Dilemma is detailed below. Reams of paper have been written on this very elegant game and, currently, its effects can be seen on many Reality TV shows that incorporate the Dilemma's basic mechanisms to force tension and backstabbing in its contestants. This is a good bit for any student of science to read although it's rare to find problems that lend themselves to such an elegant treatment. My second reason for reproducing this chapter is that the implications of the study and Dawkins's analysis have some lessons for understanding our own behaviors as a species.

Nice guys finish first (pp. 202-233)

Nice guys finish last. The phrase seems to have originated in the world of baseball, although some authorities claim priority for an alternative connotation. The American biologist Garrett Hardin used it to summarize the message of what may be called 'sociobiology' or 'selfish genery'. It is easy to see its aptness. If we translate the colloquial meaning of 'nice guy' into its Darwinian equivalent, a nice guy is an individual that assists other members of its species, at its own expense, to pass their genes on to the next generation. Nice guys, then, seem bound to decrease in numbers: niceness dies a Darwinian death. But there is another, technical, interpretation of the colloquial word 'nice'. If we adopt this definition, which is not too far from the colloquial meaning, nice guys can finish first. This more optimistic conclusion is what this chapter is about.

Remember the Grudgers of Chapter 10. These were birds that helped each other in an apparently altruistic way, but refused to help - bore a grudge against - individuals that had previously refused to help them. Grudgers came to dominate the population because they passed on more genes to future generations than either Suckers (who helped others indiscriminately, and were exploited) or Cheats (who tried ruthlessly to exploit everybody and ended up doing each other down). The story of Grudgers illustrated an important general principle, which Robert Trivers called 'reciprocal altruism'. As we saw in the example of the cleaner fish (pages 186-7), reciprocal altruism is not confined to members of a single species. It is at work in all relationships that are called symbiotic - for instance the ants milking their aphid 'cattle' (page 181). Since Chapter 10 was written, the American political scientist Robert Axelrod (working partly in collaboration with W.D. Hamilton, whose name has cropped up on so many pages of this book), has taken the idea of reciprocal altruism on in exciting new directions. It was Axelrod who coined the technical meaning of the word 'nice' to which I alluded in my opening paragraph.

Axelrod, like many political scientists, economists, mathematicians and psychologists, was fascinated by a simple gambling game called Prisoner's Dilemma. It is so simple that I have known clever men misunderstand it completely, thinking that there must be more to it! But its simplicity is deceptive. Whole shelves in libraries are devoted to the ramifications of this beguiling game. Many influential people think it holds the key to strategic defense planning, and that we should study it to prevent a third world war. As a biologist, I agree with Axelrod and Hamilton that many wild animals and plants are engaged in ceaseless games of Prisoner's Dilemma, played out in evolutionary time.

In its original, human, version, here is how the game is played. There is a 'banker', who adjudicates and pays out winnings to the two players. Suppose that I am playing against you (though, as we shall see, 'against' is precisely what we don't have to be). There are only two cards in each of our hands, labeled COOPERATE and DEFECT. To play, we each choose one of our cards and lay it face down on the table. Face down so that neither of us can be influenced by the other's move: in effect, we move simultaneously. We now wait in suspense for the banker to turn the cards over. The suspense is because our winnings depend not just on which card we have played (which we each know), but on the other player's card too (which we don't know until the banker reveals it).

Since there are 2 X 2 cards, there are four possible outcomes. For each outcome, our winnings are as follows (quoted in dollars in deference to the North American origins of the game).

Outcomes III and IV are obviously mirror images: one player does very well and the other does very badly. In outcomes I and II we do as well as one another, but I is better for both of us than II. The exact quantities of money don't matter. It doesn't even matter how many of them are positive (payments) and how many of them, if any are negative (fines). What matters, for the game to qualify as a true Prisoner's Dilemma, is their rank order. The Temptation to defect must be better than the Reward for mutual cooperation, which must be better than the Punishment for mutual defection, which must be better than the Sucker's payoff. (Strictly speaking, there is one further condition for the game to qualify as a true Prisoner's Dilemma: the average of the Temptation and Sucker payoffs must not exceed the Reward. The reason for this additional condition will emerge later.) The four outcomes are summarized in the payoff matrix in Figure A.

Now, why the 'dilemma'? To see this, look at the payoff matrix and imagine the thoughts that might go through my head as I play against you. I know that there are only two cards you can play, COOPERATE and DEFECT. Let's consider them in order. If you have played DEFECT (this means we have to look at the right hand column), the best card I could have played would have been DEFECT too. Admittedly I'd have suffered the penalty for mutual defection, but if I'd cooperated, I'd have got the Sucker's payoff which is even worse. Now let's turn to the other thing you could have done (look at the left hand column), play the COOPERATE card. Once again DEFECT is the best thing I could have done. If I had cooperated we'd both have got the rather high score of $300. But if I'd defected I'd have got even more - $500. The conclusion is that, regardless of which card you play, my best move is Always Defect.

So I have worked out by impeccable logic that, regardless of what you do, I must defect. And you, with no less impeccable logic, will work out just the same thing. So when two rational players meet, they will both defect, and both will end up with a fine or a low payoff. Yet each knows perfectly well that, if only they had both played COOPERATE, both would have obtained the relatively high reward for mutual cooperation ($300 in our example). That is why the game is called a dilemma, why it has even been proposed that there ought to be a law against it.

'Prisoner' comes from one particularly imaginary example. The currency in this case is not money but prison sentences. Two men - call them Peterson and Moriarty - are in jail, suspected of collaborating in a crime. Each prisoner, in his separate cell, is invited to betray his colleague (DEFECT ) by turning King's Evidence against him. What happens depends upon what both prisoners do, and neither knows what the other has done. If Peterson throws the blame entirely on Moriarty, and Moriarty renders the story plausible by remaining silent (cooperating with his erstwhile and, as it turns out, treacherous friend), Moriarty gets a heavy jail sentence while Peterson gets off scot-free, having yielded to Temptation to defect. If each betrays the other, both are convicted of the crime, but receive some credit for giving evidence and get a somewhat reduced, though still stiff, sentence, the Punishment for mutual defection. If both cooperate (with each other, not the authorities) by refusing to speak, there is not enough evidence to convict either of them of the main crime, and they receive a small sentence for a lesser offence, the Reward for mutual cooperation. Although it may seem odd to call a jail sentence a 'reward', that is how the men would see it if the alternative was a longer spell behind bars. You will notice that, although the 'payoffs' are not in dollars but in jail sentences, the essential features of the game are preserved (look at the rank order of desirability of the four outcomes). If you put yourself in each prisoner's place, assuming both to be motivated by rational self-interest and remembering that they cannot talk to one another to make a pact, you will see that neither has any choice but to betray the other, thereby condemning both to heavy sentences.

Is there any way out of the dilemma? Both players know that whatever their opponent does, they themselves cannot do better than DEFECT; yet both also know that, if only both had cooperated, each one would have done better. If only... if only... if only there could be some way of reaching agreement, some way of reassuring each player that the other can be trusted not to go for the selfish jackpot, some way of policing the agreement.

In the simple game of Prisoner's Dilemma, there is no way of ensuring trust. Unless at least one of the players is a really saintly sucker, too good for this world, the game is doomed to end in mutual defection with its paradoxically poor result for both players. But there is another version of the game. It is called the 'Iterated' or 'Repeated' Prisoner's Dilemma. The iterated game is more complicated, and in its complication lies hope.

The iterated game is simply the ordinary game repeated an indefinite number of times with the same players. Once again you and I face each other, with a banker sitting between. Once gain we each have a hand of just two cards, labeled COOPERATE and DEFECT. Once again we move by each playing one or other of these cards and the banker shells out, or levies fines, according to the rules given above. But now, instead of that being the end of the game, we pick up our cards and prepare for another round. The successive rounds of the game give us the opportunity to build up trust or mistrust, to reciprocate or placate, forgive or avenge. In an indefinitely long game, the important point is that we can both win at the expense of the banker, rather than at the expense of one another.

After ten rounds of the game, I could theoretically have won as much as $5,000, but only if you have been extraordinarily silly (or saintly) and played COOPERATE every single time, in spite of the fact that I was consistently defecting. More realistically, it is easy for each of us to pick up $3,000 of the banker's money by both playing COOPERATE on all ten rounds of the game. For this we don't have to be particularly saintly, because we can both see, from the other's past moves, that the other is to be trusted. We can, in effect, police each other's behavior. Another thing that is quite likely to happen is that neither of us trusts the other: we both play DEFECT for all ten rounds of the game, and the banker gains $100 in fines from each of us. Most likely of all is that we partially trust one another, and each play some mixed sequence of COOPERATE and DEFECT, ending up with some intermediate sum of money.

The birds in Chapter 10 who removed ticks from each other's feathers were playing an iterated Prisoner's Dilemma game. How is this so? It is important, you remember, for a bird to pull off his own ticks, but he cannot reach the top of his own head and needs a companion to do that for him. It would seem only fair that he should return the favor later. But this service costs a bird time and energy, albeit not much. If a bird can get away with cheating - with having his own ticks removed but then refusing to reciprocate - he gains all the benefits without paying the costs. Rank the outcomes, and you'll find that indeed we have a true game of Prisoner's dilemma. Both cooperating (pulling each other's ticks off) is pretty good, but there is still a temptation to do even better by refusing to pay the costs of reciprocating. Both defecting (refusing to pull ticks off) is pretty bad, but not so bad as putting effort into pulling another's ticks off and still ending up infested with ticks oneself. The payoff matrix is Figure B.

		What you do
		Cooperate	Defect
What I do	Cooperate	Fairly Good REWARD I get my ticks removed, although I also pay the costs of removing yours.	Very Bad SUCKER'S PAYOFF I keep my ticks, while also paying the costs of removing yours.
	Defect	Very Good TEMPTATION I get my ticks removed, and I don't pay the costs of removing yours.	Fairly Bad PUNISHMENT I keep my ticks with the small consolation of not removing yours.

Figure B. The bird tick-removing game: payoffs to me from various outcomes.

But this is only one example. The more you think about it, the more you realize that life is riddled with Iterated Prisoner's Dilemma games, not just human life but animal and plant life too. Plant life? Yes, why not? Remember that we are not talking about conscious strategies (though at times we might be), but about strategies in the 'Maynard Smithian' sense, strategies of the kind that genes might preprogram. Later we shall meet plants, various animals and even bacteria, all playing the game of Iterated Prisoner's Dilemma. Meanwhile, let's explore more fully what is so important about iteration.

Unlike the simple game, which is rather predictable in that DEFECT is the only rational strategy, the iterated version offers plenty of strategic scope. In the simple game there are only two possible strategies, COOPERATE and DEFECT. Iteration, however, allows lots of conceivable strategies, and it is by no means obvious which one is best. The following, for instance, is just one among thousands 'cooperate most of the time, but on a random 10 percent of rounds throw in a defect'. Or strategies might be conditional upon the past history of the game. My 'Grudger' is an example of this; it has a good memory for faces, and although fundamentally cooperative it defects if the other player has ever defected before. Other strategies might be more forgiving and have shorter memories.

Clearly the strategies available in the iterated game are limited only by our ingenuity. Can we work out which is best? This was the task that Axelrod set himself. He had the entertaining idea of running a competition, and he advertised for experts in games theory to submit strategies. Strategies, in this sense, are preprogrammed rules for action, so it was appropriate for contestants to send in their entries in computer language. Fourteen strategies were submitted. For good measure Axelrod added a fifteenth, called Random, which simply played COOPERATE and DEFECT randomly, and served as a kind of baseline 'non-strategy': if a strategy can't do better than Random, it must be pretty bad.

Axelrod translated all 15 strategies into one common programming language, and set them against one another in one big computer. Each strategy was paired off in turn with every other one (including a copy of itself) to play Iterated Prisoner's Dilemma. Since there were 15 strategies, there were 15 X 15 or 225 separate games going on in the computer. When each pairing had gone through 200 moves of the game, the winnings were totaled up and the winner declared.

We are not concerned with which strategy won against any particular opponent. What matters is which strategy accumulated the most 'money', summed over all its 15 pairings. 'Money' means simply 'points', awarded according to the following scheme: mutual Cooperation, 3 points; Temptation to defect, 5 points; Punishment for mutual defection, 1 point (equivalent to a light fine in our earlier game); Sucker's payoff, 0 points (equivalent to a heavy fine in our earlier game).

Figure C: Axelrod's computer tournament: payoffs to me from various outcomes

The maximum possible score that any strategy could achieve was 15,000 (200 rounds at 5 points per round, for each of 15 opponents). The minimum possible score was 0. Needless to say, neither of these two extremes was realized. The most that a strategy can realistically hope to win in an average one of its 15 pairings cannot be much more than 600 points. That is what two players would each receive if they both consistently cooperated, scoring 3 points for each of the 200 rounds of the game. If one of them succumbed to the temptation to defect, it would very probably end up with fewer points than 600 because of retaliation by the other player (most of the submitted strategies had some kind of retaliatory behavior built into them). We can use 600 as a kind of benchmark for a game, and express all scores as a percentage of this benchmark. On this scale it is theoretically possible to score up to 166 per cent (1,000 points), but in practice no strategy's average score exceeded 600.

Remember that the 'players' in the tournament were not humans but computer programs, preprogrammed strategies. Their human authors played the same role as genes programming bodies (think of Chapter 4's computer chess and the Andromeda computer). You can think of the strategies as miniature 'proxies' for their authors. Indeed, one author could have submitted more than one strategy (although it would have been cheating - and Axelrod would presumably not have allowed it - for an author to 'pack' the competition with strategies, one of which received the benefits of sacrificial cooperation from the others).

Some ingenious strategies were submitted, though they were, of course, far less ingenious than their authors. The winning strategy, remarkably, was the simplest and superficially least ingenious of all. It was called Tit for Tat, and was submitted by Professor Anatol Rapoport, a well-known psychologist and games theorist from Toronto. Tit for Tat begins by cooperating on the first move and thereafter simply copies the previous move of the other player.

How might a game involving Tit for Tat proceed? As ever, what happens depends upon the other player. Suppose, first, that the other player is also Tit for Tat (remember that each strategy played against copies of itself as well as against the other 14). Both Tit for Tats begin by cooperating. In the next move, each player copies the other's previous move, which was COOPERATE. Both continue to COOPERATE until the end of the game, and both end up with the full 100 per cent 'benchmark' score of 600 points.

Now suppose Tit for Tat plays against a strategy called Naive Prober. Naive Prober wasn't actually entered in Axelrod's competition, but it is instructive nevertheless. It is basically identical to Tit for Tat except that, once in a while, say on a random one in ten moves, it throws in a gratuitous defection and claims the high Temptation score. Until Naive Prober tries one of its probing defections the players might as well be two Tit for Tats. A long and mutually profitable sequence of cooperation seems set to run its course, with a comfortable 100 per cent benchmark score for both players. But suddenly, without warning, say on the eighth move, naive Prober defects. Tit for Tat, of course, has played COOPERATE on this move, and so is landed with the Sucker's payoff of 0 points. Naive Prober appears to have done well, since it has obtained 5 points from that move. But in the next move Tit for Tat 'retaliates'. It plays DEFECT, simply following its rule of imitating the opponent's previous move. Naive Prober meanwhile, blindly following its own built-in copying rule, has copied its opponent's COOPERATE move. So it now collects the Sucker's payoff of 0 points, while Tit for Tat gets the high score of 5. In the next move, Naive Prober - rather unjustly one might think - 'retaliates' against Tit for Tat's defection. And so the alternation continues. During these alternating runs both players receive on average 2.5 points per move (the average of 5 and 0). This is lower than the steady 3 points per move that both players can amass in a run of mutual cooperation (and, by the way, this is the reason for the 'additional condition' left unexplained on page 204). So, when Naive Prober plays against Tit for Tat, both do worse than when Tit for Tat plays against another Tit for Tat. And when Naive Prober plays against another Naive Prober, both tend to do, if anything, even worse still, since runs of reverberating defection tend to get started earlier.

Now consider another strategy, called Remorseful Prober. Remorseful Prober is like Naive Prober, except that it takes active steps to break out of runs of alternating recriminations. To do this it needs a slightly longer 'memory' than either Tit for Tat or Naive Prober. Remorseful Prober remembers whether it has just spontaneously defected, and whether the result was prompt retaliation. If so, it 'remorsefully' allows its opponent 'one free hit' without retaliating. This means that runs of mutual recrimination are nipped in the bud. If you now work through an imaginary game between Remorseful Prober and Tit for Tat, you'll find that runs of would-be mutual retaliation are promptly scotched. Most of the game is spent in mutual cooperation, with both players enjoying the consequent generous score. Remorseful does better against Tit for Tat than Naive Prober does, though not as well as Tit for Tat does against itself.

Some of the strategies entered in Axelrod's tournament were much more sophisticated than either remorseful Prober or Naive Prober, but they too ended up with fewer points, on average, than simple Tit for Tat. Indeed the least successful of all the strategies (except Random) was the most elaborate. It was submitted by 'Name withheld' - a spur to pleasing speculation: Some eminence grise in the Pentagon? The head of the CIA? Henry Kissinger? Axelrod himself? I suppose we shall never know.

It isn't all that interesting to examine the details of the particular strategies that were submitted. This isn't a book about the ingenuity of computer programmers. It is more interesting to classify strategies according to certain categories, and examine the success of these broader divisions. The most important category that Axelrod recognizes is 'nice'. A nice strategy is defined as one that is never the first to defect. Tit for Tat is an example. It is capable of defecting, but it does so only in retaliation. Both Naive Prober and Remorseful Prober are nasty strategies because they sometimes defect, however rarely, when not provoked. Of the 15 strategies entered in the tournament, 8 were nice. Significantly, the 8 top-scoring strategies were the very same 8 nice strategies, the 7 nasties trailing well behind. Tit for Tat obtained an average of 504.5 points: 84% of our benchmark of 600 and a good score. The other nice strategies scored only slightly less, with scores ranging from 83.4% down to 78.6%. There is a big gap between this score and the 66.8 per cent obtained by Graaskamp, the most successful of all the nasty strategies. It seems pretty convincing that nice guys do well in this game.

Another of Axelrod's technical terms is 'forgiving'. A forgiving strategy is one that, although it may retaliate, has a short memory. It is swift to overlook old misdeeds. Tit for Tat is a forgiving strategy. It raps a defector over the knuckles instantly but, after that, lets bygones be bygones. Chapter 10's Grudger is totally unforgiving. Its memory lasts the entire game. It never forgets a grudge against a player who has ever defected against it, even once. A strategy formally identical to Grudger was entered in Axelrod's tournament under the name of Friedman, and it didn't do particularly well. Of all the nice strategies (note that it is technically nice, although it is totally unforgiving), Grudger/Friedman did next to worst. The reason unforgiving strategies don't do very well is that they can't break out of runs of mutual recrimination, even when their opponent is 'remorseful'.

It is possible to be even more forgiving than Tit for Tat. Tit for Two Tats allows its opponents two defections in a row before it eventually retaliates. This might seem excessively saintly and magnanimous. Nevertheless Axelrod worked out that, if only somebody had submitted Tit for Two Tats, it would have won the tournament. This is because it is so good at avoiding runs of mutual recrimination.

So, we have identified two characteristics of winning strategies: niceness and forgivingness. This almost utopian-sounding conclusion - that niceness and forgivingness pay - came as a surprise to many of the experts, who had tried to be too cunning by submitting subtly nasty strategies; while even those who had submitted nice strategies had not dared anything so forgiving as Tit for Two Tats.

Axelrod announced a second tournament. He received 62 entries and again added Random, making 63 in all. This time, the exact number of moves per game was not fixed at 200 but was left open, for a good reason that I shall come to later. We can still express scores as a percentage of the 'benchmark', or 'always cooperate' score, even though that benchmark needs more complicated calculation and is no longer a fixed 600 points.

Programmers in the second tournament had all been provided with the results of the first, including Axelrod's analysis of why Tit for Tat and other nice and forgiving strategies had done so well. It was only to be expected that the contestants would take note of this background information, in one way or another. In fact, they split into two schools of thought. Some reasoned that niceness and forgivingness were evidently winning qualities, and they accordingly submitted nice, forgiving strategies. John Maynard Smith went so far as to submit the super-forgiving Tit for Two Tats. The other school of thought reasoned that lots of their colleagues, having read Axelrod's analysis, would now submit nice, forgiving strategies. They therefore submitted nasty strategies, trying to exploit these anticipated softies!

But once again nastiness didn't pay. Once again, Tit for Tat, submitted by Anatol Rapoport, was the winner, and it scored a massive 96 per cent of the benchmark score. And again nice strategies, in general, did better than nasty ones. All but one of the top 15 strategies were nice, and all but one of the bottom 15 were nasty. But although the saintly Tit for Two Tats would have won the first tournament if it had been submitted, it did not win the second. This was because the field now included more subtle nasty strategies capable of preying ruthlessly upon such an out-and-out softy.

This underlies an important point about these tournaments. Success for a strategy depends upon which other strategies happen to be submitted. This is the only way to account for the difference between the second tournament, in which Tit for Two Tats was ranked well down the list, and the first tournament, which Tit for Two Tats would have won. But, as I said before, this is not a book about the ingenuity of computer programmers. Is there an objective way in which we can judge which is the truly best strategy, in a more general and less arbitrary sense? Readers of earlier chapters will already be prepared to find the answer in the theory of evolutionarily stable strategies.

I was one of those to whom Axelrod circulated his early results with an invitation to submit a strategy for the second tournament. I didn't do so, but I did make another suggestion. Axelrod had already begun to think in ESS [Evolutionarily Stable Strategy, p. 69] terms, but I felt that this tendency was so important that I wrote to him suggesting that he should get in touch with W.D. Hamilton, who was then, though Axelrod didn't know it, in a different department of the same university, the University of Michigan. He did indeed immediately contact Hamilton, and the result of their subsequent collaboration was a brilliant joint paper published in the journal Science in 1981, a paper that won the Newcomb Cleveland Prize of the American Association for the Advancement of Science. In addition to discussing some delightfully way-out biological examples of iterated prisoner's dilemmas, Axelrod and Hamilton gave what I regard as due recognition to the ESS approach.

Contrast the ESS approach with the 'round-robin' system that Axelrod's two tournaments followed. A round-robin is like a football league. Each strategy was matched against each other strategy an equal number of times. The final score of a strategy was the sum of the points it gained against all the other strategies. To be successful in a round-robin tournament, therefore, a strategy has to be a good competitor against all the other strategies that people happen to have submitted. Axelrod's name for a strategy that is good against a wide variety of other strategies is 'robust'. Tit for Tat turned out to be a robust strategy. But the set of strategies that people happen to have submitted is an arbitrary set. This was the point that worried us above. It just so happened that in Axelrod's original tournament about half the entries were nice. Tit for Tat won in this climate, and Tit for Two Tats would have won in this climate if it had been submitted. But suppose that nearly all the entries had just happened to be nasty. This could very easily have occurred. After all, 6 out of the 14 strategies submitted were nasty. If 13 of them had been nasty, Tit for Tat wouldn't have won. The 'climate' would have been wrong for it. Not only the money won, but the rank order of success among strategies, depends upon which strategies happen to have been submitted; depends, in other words, upon something as arbitrary as human whim. How can we reduce this arbitrariness? By 'thinking ESS'.

The important characteristic of an evolutionarily stable strategy, you will remember from earlier chapters, is that it carries on doing well when it is already numerous in the population of strategies. To say that Tit for Tat, say, is an ESS, would be to say that Tit for Tat does well in a climate dominated by Tit for Tat. This could be seen as a special kind of 'robustness'. As evolutionists we are tempted to see it as the only kind of robustness that matters. Why does it matter so much? Because, in the world of Darwinism, winnings are not paid out as money; they are paid out as offspring. To a Darwinian, a successful strategy is one that has become numerous to the population of strategies. For a strategy to remain successful, it must do well specifically when it is numerous, that is in a climate dominated by copies of itself.

Axelrod did, as a matter of fact, run a third round of his tournament as natural selection might have run it, looking for an ESS. Actually he didn't call it a third round, since he didn't solicit new entries but used the same 63 as for Round 2. I find it convenient to treat it as Round 3, because I think it differs from the two 'round-robin' tournaments more fundamentally than the two round-robin tournaments differ from each other.

Axelrod took the 63 strategies and threw them again into the computer to make 'generation 1' of an evolutionary succession. In 'generation 1', therefore, the 'climate' consisted of an equal representation of all 63 strategies. At the end of generation 1, winnings to each strategy were paid out, not as 'money' or 'points', but as offspring, identical to their (asexual) parents. As generations went by, some strategies became scarcer and eventually went extinct. Other strategies became more numerous. As the proportions changed, so, consequently, did the 'climate' in which future moves of the game took place.

Eventually, after about 1,000 generations, there were no further changes in proportions, no further changes in climate. Stability was reached. Before this, the fortunes of the various strategies rose and fell, just as in my computer simulation of the Cheats, Suckers, and Grudgers. Some of the strategies started going extinct from the start, and most were extinct by generation 200. Of the nasty strategies, one or two of them began by increasing in frequency, but their prosperity, like that of Cheat in my simulation, was short-lived. The only nasty strategy to survive beyond generation 200 was one called Harrington. Harrington's fortunes rose steeply for about the first 150 generations. Thereafter it declined rather gradually, approaching extinction around generation 1,000. Harrington did well temporarily for the same reason as my original Cheat did. It exploited softies like Tit for Two Tats (too forgiving) while these were still around. Then, as the softies were driven extinct, Harrington followed them, having no easy prey left. The field was free for 'nice' but 'provacable' strategies like Tit for Tat.

Tit for Tat itself, indeed, came out top in five out of six runs of Round 3, just as it had in Rounds 1 and 2. Five other nice but provacable strategies ended up nearly as successful (frequent in the population) as Tit for Tat; indeed, one of them won the sixth run. When all the nasties had been driven extinct, there was no way in which any of the nice strategies could be distinguished from Tit for Tat or from each other, because they all, being nice, simply played COOPERATE against each other.

A consequence of this indistinguishability is that, although Tit for Tat seems like an ESS, it is strictly not a true ESS. To be an ESS, remember, a strategy must not be invadable, when it is common, by a rare, mutant strategy. Now it is true that Tit for Tat cannot be invaded by any nasty strategy, but another nice strategy is a different matter. As we have just seen, in a population of nice strategies they will all look and behave exactly like one another: they will all COOPERATE all the time. So any other nice strategy, like the totally saintly Always Cooperate, although admittedly it will not enjoy a positive selective advantage over Tit for Tat, can nevertheless drift into the population without being noticed. So technically Tit for Tat is not an ESS.

You might think that since the world stays just as nice, we could as well regard Tit for Tat as an ESS. But alas, look what happens next. Unlike Tit for Tat, Always Cooperate is not stable against invasion by nasty strategies such as Always Defect. Always Defect does well against Always Cooperate, since it gets the high 'Temptation' score every time. Nasty strategies like Always Defect will come in to keep down the numbers of too nice strategies like Always Cooperate.

But although Tit for Tat is strictly speaking not a true ESS, it is probably fair to treat some sort of mixture of basically nice but retaliatory 'Tit for Tat-like' strategies as roughly equivalent to an ESS in practice. Such a mixture might include a small admixture of hastiness. Robert Boyd and Jeffrey Lorberbaum, in one of the more interesting follow-ups to Axelrod's work, looked at a mixture of Tit for Two Tats and a strategy called Suspicious Tit for Tat. Suspicious Tit for Tat is technically nasty, but it is not very nasty. It behaves just like Tit for Tat itself after the first move, but - this is what makes it technically nasty - it does defect on the very first move of the game. In a climate entirely dominated by Tit for Tat, Suspicious Tit for Tat does not prosper, because its initial defection triggers an unbroken run of mutual recrimination. When it meets a Tit for Two Tats player, on the other hand, Tit for Two Tat's greater forgivingness nips this recrimination in the bud. Both players end the game with at least the 'benchmark', all C, score and with Suspicious Tit for Tat scoring a bonus for its initial defection. Boyd and Lorberbaum showed that a population of Tit for Tat could be invaded, evolutionarily speaking, by a mixture of Tit for Two Tats and Suspicious Tit for Tat, the two prospering in each other's company. This combination is almost certainly not the only combination that could invade in this way. There are probably lots of mixtures of slightly nasty strategies with nice and very forgiving strategies that are together capable of invading. Some might see this as a mirror for familiar aspects of human life.

Axelrod recognized that Tit for Tat is not strictly an ESS, and he therefore coined the phrase 'collectively stable strategy' to describe it. As in the case of true ESSs, it is possible for more than one strategy to be collectively stable at the same time. And again, it is a matter of luck which one comes to dominate a population. Always Defect is also stable, as well as Tit for Tat. In a population that has already come to be dominated by Always Defect, no other strategy does better. We can treat the system as bistable, with Always Defect being one of the stable points, Tit for Tat (or some mixture of mostly nice, retaliatory strategies) the other stable point. Whichever stable point comes to dominate the population first will tend to stay dominant.

But what does 'dominate' mean, in quantitative terms? How many Tit for Tats must there be in order for Tit for Tat to do better than Always Defect? That depends upon the detailed payoffs that the banker has agreed to shell out in this particular game. All that we can say in general is that there is a critical frequency, a knife-edge. On one side of the knife-edge the critical frequency of Tit for Tat is exceeded, and selection will favor more and more Tit for Tats. On the other side of the knife-edge the critical frequency of Always Defect is exceeded, and selection will favor more and more Always Defects. We met the equivalent of this knife-edge, you will remember, in the story of the Grudgers and Cheats in Chapter 10.

It obviously matters, therefore, on which side of the knife-edge a population happens to start. And we need to know how it might happen that a population could occasionally cross from one side of the knife-edge to the other. Suppose we start with a population already sitting on the Always Defect side. The few Tit for Tat individuals don't meet each other often enough to be of mutual benefit. So natural selection pushes the population even further towards the Always Defect extreme. If only the population could just manage, by random drift, to get itself over the knife-edge, it could coast down the slope to the Tit for Tat side, and everyone would do much better at the banker's (or nature's) expense. But of course populations have no group will, no group intention or purpose. They cannot strive to leap the knife-edge. They will cross it only if the undirected forces of nature happen to lead them across.

How could this happen? One way to express the answer is that it might happen by 'chance'. But 'chance' is just a word expressing ignorance. It means 'determined by some as yet unknown, or unspecified, means'. We can do a little better than 'chance'. We can try to think of practical ways in which a minority of Tit for Tat individuals might happen to increase to the critical mass. This amounts to a quest for possible ways in which Tit for Tat individuals might happen to cluster together in sufficient numbers that they can all benefit at the banker's expense.

This line of thought seems to be promising, but it is rather vague. How exactly might mutually resembling individuals find themselves clustered together in local aggregations? In nature, the obvious way is through genetic relatedness - kinship. Animals of most species are likely to find themselves living close to their sisters, brothers and cousins, rather than to random members of the population. This is not necessarily through choice. It follows automatically from 'viscosity' in the population. Viscosity means any tendency for individuals to continue living close to the place where they were born. For instance, through most of history, and in most parts of the world (though not, as it happens, in our modern world), individual humans have seldom strayed more than a few miles from their birthplace. As a result, local clusters of genetic relatives tend to build up. I remember visiting a remote island off the west coast of Ireland, and being struck by the fact that almost everyone on the island had the most enormous jug-handled ears. This could hardly have been because large ears suited the climate (there are strong offshore winds). It was because most of the inhabitants of the island were close kin of one another.

Genetic relatives will tend to be alike not just in facial features but in all sorts of other respects as well. For instance, they will tend to resemble each other with respect to genetic tendencies to play - or not to play - Tit for Tat. So even if Tit for Tat is rare in the population as a whole, it may still be locally common. In a local area, Tit for Tat individuals may meet each other often enough to prosper from mutual cooperation, even though calculations that take into account only the global frequency in the total population might suggest that they are below the 'knife-edge' critical frequency.

If this happens, Tit for Tat individuals, cooperating with one another in cozy little local enclaves, may prosper so well that they grow from small local clusters into larger local clusters. These local clusters may grow so large that they spread out into other areas, areas that had hitherto been dominated, numerically, by individuals playing Always Defect. In thinking of these local enclaves, my Irish island is a misleading parallel because it is physically cut off. Think, instead, of a large population in which there is not much movement, so that individuals tend to resemble their immediate neighbors more than their more distant neighbors, even though there is continuous interbreeding all over the whole area.