The Selfish Gene (33 page)

It is only a mistake in certain kinds of game. Games theorists divide games into 'zero sum' and 'nonzero sum'. A zero sum game is one in which a win for one player is a loss for the other. Chess is zero sum, because the aim of each player is to win, and this means to make the other player lose. Prisoner's Dilemma, however, is a nonzero sum game. There is a banker paying out money, and it is possible for the two players to link arms and laugh all the way to the bank.

This talk of laughing all the way to the bank reminds me of a delightful line from Shakespeare:

The first thing we do, let's kill all the lawyers.

2 Henry VI

In what are called civil 'disputes' there is often in fact great scope for cooperation. What looks like a zero sum confrontation can, with a little goodwill, be transformed into a mutually beneficial nonzero sum game. Consider divorce. A good marriage is obviously a nonzero sum game, brimming with mutual cooperation. But even when it breaks down there are all sorts of reasons why a couple could benefit by continuing to cooperate, and treating their divorce, too, as nonzero sum. As if child welfare were not a sufficient reason, the fees of two lawyers will make a nasty dent in the family finances. So obviously a sensible and civilized couple begin by going together to see one lawyer, don't they?

Well, actually no. At least in England and, until recently, in all fifty states of the USA, the law, or more strictly-and significantly-the lawyers' own professional code, doesn't allow them to. Lawyers must accept only one member of a couple as a client. The other person is turned from the door, and either has no legal advice at all or is forced to go to another lawyer. And that is when the fun begins. In separate chambers but with one voice, the two lawyers immediately start referring to 'us' and 'them'. 'Us', you understand, doesn't mean me and my wife; it means me and my lawyer against her and her lawyer. When the case comes to court, it is actually listed as 'Smith versus Smith'! It is assumed to be adversarial, whether the couple feel adversarial or not, whether or not they have specifically agreed that they want to be sensibly amicable. And who benefits from treating it as an 'I win, you lose' tussle? The chances are, only the lawyers.

The hapless couple have been dragged into a zero sum game. For the lawyers, however, the case of Smith v. Smith is a nice fat nonzero sum game, with the Smiths providing the payoffs and the two professionals milking their clients' joint account in elaborately coded cooperation. One way in which they cooperate is to make proposals that they both know the other side will not accept. This prompts a counter proposal that, again, both know is unacceptable. And so it goes on. Every letter, every telephone call exchanged between the cooperating 'adversaries' adds another wad to the bill. With luck, this procedure can be dragged out for months or even years, with costs mounting in parallel. The lawyers don't get together to work all this out. On the contrary, it is ironically their scrupulous separateness that is the chief instrument of their cooperation at the expense of the clients. The lawyers may not even be aware of what they are doing. Like the vampire bats that we shall meet in a moment, they are playing to well-ritualized rules. The system works without any conscious overseeing or organizing. It is all geared to forcing us into zero sum games. Zero sum for the clients, but very much nonzero sum for the lawyers.

What is to be done? The Shakespeare option is messy. It would be cleaner to get the law changed. But most parliamentarians are drawn from the legal profession, and have a zero sum mentality. It is hard to imagine a more adversarial atmosphere than the British House of Commons. (The law courts at least preserve the decencies of debate. As well they might, since 'my learned friend and I' are cooperating very nicely all the way to the bank.) Perhaps well-meaning legislators and, indeed, contrite lawyers should be taught a little game theory. It is only fair to add that some lawyers play exactly the opposite role, persuading clients who are itching for a zero sum fight that they would do better to reach a nonzero sum settlement out of court.

What about other games in human life? Which are zero sum and which nonzero sum? And-because this is not the same thing- which aspects of life do we perceive as zero or nonzero sum? Which aspects of human life foster 'envy', and which foster cooperation against a 'banker'? Think, for instance, about wage-bargaining and 'differentials'. When we negotiate our pay-rises, are we motivated by 'envy', or do we cooperate to maximize our real income? Do we assume, in real life as well as in psychological experiments, that we are playing a zero sum game when we are not? I simply pose these difficult questions. To answer them would go beyond the scope of this book.

Football is a zero sum game. At least, it usually is. Occasionally it can become a nonzero sum game. This happened in 1977 in the English Football League (Association Football or 'Soccer'; the other games called football-Rugby Football, Australian Football, American Football, Irish Football, etc., are also normally zero sum games). Teams in the Football League are split into four divisions. Clubs play against other clubs within their own division, accumulating points for each win or draw throughout the season. To be in the First Division is prestigious, and also lucrative for a club since it ensures large crowds. At the end of each season, the bottom three clubs in the First Division are relegated to the Second Division for the next season. Relegation seems to be regarded as a terrible fate, worth going to great efforts to avoid.

May 18th 1977 was the last day of that year's football season. Two of the three relegations from the First Division had already been determined, but the third relegation was still in contention. It would definitely be one of three teams, Sunderland, Bristol, or Coventry. These three teams, then, had everything to play for on that Saturday. Sunderland
were playing against a fourth team (whose tenure in the First Division was not in doubt). Bristol and Coventry
happened to be playing against each other. It was known that, if Sunderland lost their game, then Bristol and Coventry
needed only to draw against each other in order to stay in the First Division. But if Sunderland won, then the team relegated would be either Bristol or Coventry
, depending on the outcome of their game against each other. The two crucial games were theoretically simultaneous. As a matter of fact, however, the Bristol-Coventry game happened to be running five minutes late. Because of this, the result of the Sunderland game became known before the end of the Bristol-Coventry game. Thereby hangs this whole complicated tale.

For most of the game between Bristol and Coventry the play was, to quote one contemporary news report, 'fast and often furious', an exciting (if you like that sort of thing) ding-dong battle. Some brilliant goals from both sides had seen to it that the score was 2-all by the eightieth minute of the match. Then, two minutes before the end of the game, the news came through from the other ground that Sunderland had lost. Immediately, the Coventry team manager had the news flashed up on the giant electronic message board at the end of the ground. Apparently all 22 players could read, and they all realized that they needn't bother to play hard any more. A draw was all that either team needed in order to avoid relegation. Indeed, to put effort into scoring goals was now positively bad policy since, by taking players away from defence, it carried the risk of actually losing-and being relegated after all. Both sides became intent on securing a draw. To quote the same news report: 'Supporters who had been fierce rivals seconds before when Don Gillies fired in an 80th minute equaliser for Bristol, suddenly joined in a combined celebration. Referee Ron Challis watched helpless as the players pushed the ball around with little or no challenge to the man in possession.' What had previously been a zero sum game had suddenly, because of a piece of news from the outside world, become a nonzero sum game. In the terms of our earlier discussion, it is as if an external 'banker' had magically appeared, making it possible for both Bristol and Coventry to benefit from the same outcome, a draw.

Spectator sports like football are normally zero sum games for a good reason. It is more exciting for crowds to watch players striving mightily against one another than to watch them conniving amicably. But real life, both human life and plant and animal life, is not set up for the benefit of spectators. Many situations in real life are, as a matter of fact, equivalent to nonzero sum games. Nature often plays the role of 'banker', and individuals can therefore benefit from one another's success. They do not have to do down rivals in order to benefit themselves. Without departing from the fundamental laws of the selfish gene, we can see how cooperation and mutual assistance can flourish even in a basically selfish world. We can see how, in Axelrod's meaning of the term, nice guys may finish first.

But none of this works unless the game is iterated. The players must know (or 'know') that the present game is not the last one between them. In Axelrod's haunting phrase, the 'shadow of the future' must be long. But how long must it be? It can't be infinitely long. From a theoretical point of view it doesn't matter how long the game is; the important thing is that neither player should know when the game is going to end. Suppose you and I were playing against each other, and suppose we both knew that the number of rounds in the game was to be exactly 100. Now we both understand that the 100th round, being the last, will be equivalent to a simple one-off game of Prisoner's Dilemma. Therefore the only rational strategy for either of us to play on the 100th round will be defect, and we can each assume that the other player will work that out and be fully resolved to defect on the last round. The last round can therefore be written off as predictable. But now the 99th round will be the equivalent of a one-off game, and the only rational choice for each player on this last but one game is also defect. The 98th round succumbs to the same reasoning, and so on back. Two strictly rational players, each of whom assumes that the other is strictly rational, can do nothing but defect if they both know how many rounds the game is destined to run. For this reason, when games theorists talk about the Iterated or Repeated Prisoner's Dilemma game, they always assume that the end of the game is unpredictable, or known only to the banker.

Even if the exact number of rounds in the game is not known for certain, in real life it is often possible to make a statistical guess as to how much longer the game is likely to last. This assessment may become an important part of strategy. If I notice the banker fidget and look at his watch, I may well conjecture that the game is about to be brought to an end, and I may therefore feel tempted to defect. If I suspect that you too have noticed the banker fidgeting, I may fear that you too may be contemplating defection. I will probably be anxious to get my defection in first. Especially since I may fear that you are fearing that I. ..

The mathematician's simple distinction between the one-off Prisoner's Dilemma game and the Iterated Prisoner's Dilemma game is too simple. Each player can be expected to behave as if he possessed a continuously updated estimate of how long the game is likely to go on. The longer his estimate, the more he will play according to the mathematician's expectations for the true iterated game: in other words, the nicer, more forgiving, less envious he will be. The shorter his estimate of the future of the game, the more he will be inclined to play according to the mathematician's expectations for the one-off game: the nastier, and less forgiving will he be. Axelrod draws a moving illustration of the importance of the shadow of the future from a remarkable phenomenon that grew up during the First World War, the so-called live-and-let-live system. His source is the research of the historian and sociologist Tony Ashworth. It is quite well known that at Christmas British and German troops briefly fraternized and drank together in no-man's-land. Less well known, but in my opinion more interesting, is the fact that unofficial and unspoken nonaggression pacts, a 'live-and-let-live' system, flourished all up and down the front lines for at least two years starting in 1914. A senior British officer, on a visit to the trenches, is quoted as being astonished to observe German soldiers walking about within rifle range behind their own line. 'Our men appeared to take no notice. I privately made up my mind to do away with that sort of thing when we took over; such things should not be allowed. These people evidently did not know there was a war on. Both sides apparently believed in the policy of “live-and-let-live”.' The theory of games and the Prisoner's Dilemma had not been invented in those days but, with hindsight, we can see pretty clearly what was going on, and Axelrod provides a fascinating analysis. In the entrenched warfare of those times, the shadow of the future for each platoon was long. That is to say, each dug-in group of British soldiers could expect to be facing the same dug-in group of Germans for many months. Moreover, the ordinary soldiers never knew when, if ever, they were going to be moved; army orders are notoriously arbitrary, capricious and incomprehensible to those receiving them. The shadow of the future was quite long enough, and indeterminate enough, to foster the development of a Tit for Tat type of cooperation. Provided, that is, that the situation was equivalent to a game of Prisoner's Dilemma.

To qualify as a true Prisoner's Dilemma, remember, the payoffs have to follow a particular rank order. Both sides must see mutual cooperation (CC) as preferable to mutual defection. Defection while the other side cooperates (DC) is even better if you can get away with it. Cooperation while the other side defects (CD) is worst of all. Mutual defection (DD) is what the general staff would like to see. They want to see their own chaps, keen as mustard, potting Jerries (or Tommies) whenever the opportunity arises.

Mutual cooperation was undesirable from the generals' point of view, because it wasn't helping them to win the war. But it was highly desirable from the point of view of the individual soldiers on both sides. They didn't want to be shot. Admittedly-and this takes care of the other payoff conditions needed to make the situation a true Prisoner's Dilemma-they probably agreed with the generals in preferring to win the war rather than lose it. But that is not the choice that faces an individual soldier. The outcome of the entire war is unlikely to be materially affected by what he, as an individual, does. Mutual cooperation with the particular enemy soldiers facing you across no-man's-land most definitely does affect your own fate, and is greatly preferable to mutual defection, even though you might, for patriotic or disciplinary reasons, marginally prefer to defect (DC) if you could get away with it It seems that the situation was a true prisoner's dilemma. Something like Tit for Tat could be expected to grow up, and it did.