The Prisoner's Dilemma (17 page)

Hume stopped for a moment and looked into the fire. He had given the Dilemma a deal of thought these past two weeks and he now wished to bring the sterility of their repetitive contests to an end.

‘Let me give you another example,' he continued looking back to Dunbeath, ‘you'll recall that in our grandfathers' day the English and the Dutch spent ruinous sums on great navies to protect their commercial interests as if the gain of one would be the loss of the other. But we learnt, did we not, that it was actually due to the competition between them that world trade grew. It became evident that it was not the
share
of the trade that one country achieved that mattered so much as the
growth
in the custom itself. Both countries could be winners – in fact, the evidence was that they were.'

‘You may be right in both your examples,' Dunbeath replied thoughtfully, ‘but nonetheless it is the rational player in these games – as in life itself – who will do better when he plays an irrational one. These leaps of logic you describe may be obvious to the distinguished moral philosopher I am addressing here at my table but they will escape the normal man. They are therefore not present in everyday exchanges. Far from it, it is the calculating fellow who will always beat the naïve.'

Hume sighed heavily and his shoulders sagged.

‘Sophie, can you help me here? I really don't think this is a conclusion that I alone have reached. I think we only have to look at how people go about their daily lives to see that.'

Sophie looked down at the scores.

‘Perhaps it's easier for me to give an opinion as I haven't been caught up in the competition of the game,' she replied, ‘but it must be plain that the answer about how to play depends on what one's aim is. If one wants to gain from society by building the order and reliability of that society, and therefore to profit from it, then co-operation must be the correct strategy. Essentially the way I see it is that, over time, one is not escaping the hangman's noose of a one-time Prisoner's Dilemma but instead looking for people to play high scoring games with – to live to fight another day rather than to be beaten. To win wars not battles. And to do this one has to recognise that it's the
collective
score that matters more than the individual's, just as keeping silent would have helped both prisoners if they could but have trusted each other.'

Hume nodded at this and smiled encouragingly at her as she continued.

‘Unlike the prisoners and your attempt to replicate the two cells with your book barrier – in real life we
do
communicate. In reality we remember how people have behaved in the past and how they are likely to behave in the future. And therefore we can decide who we want to deal with. On the other hand, the key to
dealing with constant defectors is to decide not to play with them. To avoid them and find other partners instead. Once one's found co-operative people then stable relationships and stable societies can be formed that will bring real benefits to the individual. That is how a man wins, not by constantly trying to beat someone in every single exchange. This much seems evident to me. However, it also seems that the real problem then arises with people who take advantage of a society in which
others
are co-operating.'

Hume and Dunbeath both looked at her with interest.

‘What do you mean by that Miss Kant?'

‘Well, let me give you an example,' she continued, becoming more confident that the two men were genuine in their wish to hear her views. ‘Take, for instance, a ferry. It crosses a piece of open water. The price of the passage is low, say it's a penny. The ferryman depends on this income to provide the service, to keep the boat seaworthy, feed his family and so on. The people in this little community, of course, equally depend on a reliable and efficient way of making the crossing. It's late one evening and the ferry is full. It's about to leave when a man silently jumps on without paying and without the ferryman noticing. Now, will the ferryman be impoverished by this? No – don't forget, he was leaving anyway. But this defector – let's call him a ‘free rider' because he's travelling for nothing – has gained an advantage from the co-operation of others, from people who
have
paid.

‘This free rider is simply doing something that we might all be tempted to do in the same circumstances – but if
everyone
actually behaved like this then it would be disastrous for society. In fact, I'd go so far as to say that any situation in which one would be tempted to do something, but one also knows that it would be catastrophic if everyone did the same thing, is likely to be a form of Prisoner's Dilemma.'

David Hume was listening closely, clearly very intrigued by the story. He scratched his head and then lifted a hand.

‘I hope you don't mind me adding to your argument, Sophie,' he said, ‘but I can see an important insight into society's ways here. You see, if the free rider was seen by the other passengers when he jumped onto the ferry then he's known to be the thief that he is. He's given up his right to be trusted. For the sake of a penny!

‘But you're not alone in drawing a conclusion from this kind of tale, Sophie,' he continued, straightening his beautiful coat with the pleasure of the conversation, ‘I was hearing the other day about something one of the French thinkers had written. He was describing a stag hunt in which the men of a village had formed a circle and were closing in on a fine specimen they'd surrounded. Suddenly one of the men saw a rabbit and left the circle to catch it. The man's logic was understandable at that moment because the rabbit would feed his family. But the stag rushed through the gap he'd left and was lost to the village. Would the rabbit feed the group? No. But the stag would have done. And no individual would have been able to kill the stag on his own.

‘Even though one can see why the lure of the short term reward of catching the rabbit was so attractive to him, this defector would have eaten his full if the stag had been caught. And he wouldn't have earned the disgust of his neighbours. The logic of his defection is now seen to be very different from the impact of the price he was made to pay for his actions later.'

Hume took a deep pull from the whisky he had in front of him.

‘Surely both stories are making the same point,' he continued as he put the glass down. ‘Where one has a society based on co-operation like the paying ferry customers or the stag hunters then the selfish man will defect easily – but at a considerable price. Society may be the loser but society will respond by seeing him for what he is. And people won't trust him in future. The Frenchman's interpretation was that because the man would have
made the right decision for himself but the wrong one for the group, the story showed that ever expecting social co-operation is absurd. But surely that's wrong? Surely the right view is that it simply shows how important it is for society to exclude free riders and rabbit grabbers?'

Dunbeath grimaced.

‘Exclude them? Perhaps shooting them would be more telling.'

Hume smiled but decided to avoid rising to Dunbeath's provocation. Instead he nodded and went quickly on.

‘Very well, then, let me give you another parable which amused me when I thought of it. You have a group of people. A rich man has gathered them together in a room and he says to them …‘I shall give each of you £50 if you can all stay quiet for just sixty minutes. But if someone breaks the silence and shouts out during that time then he alone will get £20 and the rest of you will get nothing!' The rich man turns over an hourglass and the group stands, watching the sands as they run through, all of them tense, willing the flow to come to an end. Time passes. Now, what would you do if you were one of those people? Obviously you'd think to yourself that you'd be better off if everyone kept their mouths shut. But then you'd think again …what if one of these people gets it into his head that he wants to be superior to the rest of us? What if he thinks it's more important to get something and for the rest of us to get nothing? In fact, he'll think he's been clever. Got an advantage over us. And then you think – well, if that's what other people will be thinking, why don't I be the clever one instead? You may want the £50, you may want to be a good member of the group. But can you risk someone else not thinking that he'll outsmart you all? And the £20 is certain, the £50 is at risk. What do you do? My friends, if you're thinking intelligently, you'd shout.'

Hume laughed, pleased to see the way that Dunbeath was evidently thinking about how he would have behaved.

‘This little tale,' he continued, ‘the free rider story and the Prisoner's Dilemma, all seem to me to be revealing a great insight. They are surely all versions of what happens when collective and individual interests are in conflict. But what the Dilemma and these other little stories show is that the winning strategy is the one based on
seeing the future
. It is the ability to have this vision, to be able to use one's imagination and to weigh things up, that separates man from the animals. Man can imagine the future. He can see the consequences of his actions and the likely actions of others and can shape his behaviour accordingly. It is why he lives in hope – and frequently in tears. But if you take the mechanism of the Dilemma, he's able to see that rewards come to those who co-operate. In other words he wishes to appear to be unselfish, to be co-operative, but only because he selfishly wants the rewards that doing so will bring!'

Hume came to a sudden, abrupt stop. He appeared to retreat inside himself, stunned, apparently silenced by the realisation of what he'd just said. Then he looked upwards towards the ceiling, deep in thought. A moment later he still seemed so struck by his own conclusion that he got to his feet and stood, fidgeting by his chair. Once again he said, murmuring slowly, more to himself than to the others,
‘one wishes to appear to be unselfish but only because one selfishly wants the rewards that doing so will bring.'

He gently shook his head and smiled in astonishment at what he'd heard himself say. There was a silence from Dunbeath and Sophie as they looked over at him and Hume shook his head again and smiled. They both watched as he then walked to the window, absorbed in his thinking, to where a long sideboard stood with a decanter of whisky on it. He refilled his glass and then looked out of the window at the darkening sky.

‘I think a big storm is brewing,' he said abstractedly, still astonished and excited by his insight. He gazed over at the clouds massing to the east and was about to turn back to the room when he glanced down at the beach. It was then that he saw
Zweig staring intently up at him.

‘Hello,' he called out over his shoulder, ‘what's going on here? You have a strange watcher down here on the beach, Dunbeath. What do you imagine his game is?'

Sophie and Dunbeath came to the window to see what Hume was talking about.

Sophie shrank back when she saw that it was Zweig but Dunbeath became immediately aggressive.

‘It's that fool of a ship's captain,' he said angrily.

‘Which ship?' asked Hume.

‘The one that blew up.'

‘But I thought everybody but Sophie had perished. How on earth did he escape from the blast? Was he blown here?'

‘No, he must have swum ashore,' muttered Dunbeath without thinking. ‘I saw him through my big telescope when he was on deck.'

Sophie looked closely at Dunbeath.

‘Oh, you had seen him before then. You told me you didn't know who he was when you took the Domenico Salva from him on the dunes.'

Dunbeath said nothing and Hume spoke quickly to save the tension from developing.

‘Have you ever seen such an intensity in someone? The man seems to be on fire. What do you think he wants?'

But Dunbeath simply wheeled away from the window. The anger that had so obviously flared up in him came as much from having Sophie cross-question him as from having Zweig make such a provocative and public invasion of his territory.

‘Come away from the window,' he said tersely, ‘we don't need to concern ourselves with him. I dare say the next tide will wash him away.

Once Zweig had seen first Hume and then the others come to the window he'd allowed himself the minutest of satisfied smiles, only too aware that the game was now afoot.

It was over four hours since he had taken up his position but not once had he wavered in his concentration. He knew that he never could. Again and again he summoned up the meditation techniques he'd learned in the East, shown to him when he'd been trading between the Baltic and the Straits of Malacca, bringing back shiploads of the fashionable blue and white china that the Russian market so admired. The monks he'd spent time with there had taught him their secret ways to a mental process so intense in its focus that it never allowed the mind to drift. So far he had succeeded but the ordeal was just a few hours old and he knew that he was still in the foothills of the mountain he had to climb.

Night was falling and a fresh wind had sprung up and with it the portent of heavy rain. He was pleased – the weather would stiffen his resolve and a rainstorm would keep him fresh for the task.

* * * 

In the castle Sophie woke with a start, a chill at her heart and the sick memory of the sight of Zweig on the dunes clouding her dreams. She turned over yet again. A further five minutes passed before she admitted to herself that sleep would never return while she lay fretting over whether he was still there.

She lit her candle and threw back the heavy covers, then pulled a shawl over her shoulders and walked to the window. Even before she reached it she knew from the shriek of the wind and the mad pattering of the rain that a wild storm had broken.

She pulled back the curtain to see the windows being lashed
by the violent squall. She put the candle to one side and then cupped her hands to the pane to look out through the glass. As she did so her eyes gradually adjusted to the dark and she took in Zweig in the distance, drenched, his clothes clinging to his iron physique, impervious to the slashing deluge. Then with a sick shock she realised that he was staring directly back at her, quite still, focusing solely on her window.

She shuddered and drew the curtains again.

Zweig had indeed seen her – first the flash of her candle and then the whiteness of her face. He was also pleased to see the speed with which she'd retreated, so obviously shocked at the sight.

‘Three. Five,' he murmured to himself, counting the floors and then the position of her window from the castle's end.

* * * 

The next morning opened fair with a drying wind and a warm high sun that promised much for the day.

Major Sharrocks arrived, coming up quietly behind his sentry.

‘A wet night, trooper,' he said without much sympathy, ‘what's happening? Is he still there then?'

‘Yes, sir,' replied the redcoat putting down his telescope, ‘never moved a muscle. Been there all night, just staring like.'

‘What the hell's going on?' said Sharrocks, testily. ‘Something's happening here – and I mean to find out what.'

* * * 

Sophie had slept little. In the early hours she'd tossed and turned before deciding eventually that there was nothing she could do about Zweig and came to the conclusion instead that she should immerse herself in the Dilemma as a distraction. She'd risen and gone to the dining room and five hours later she was there still,
surrounded by pages of mathematical workings and wrapped in her extraordinary concentration. So deep was she in her calculations that she didn't notice as David Hume wandered into the room in the hope of breakfast, but she looked up as he peered over her shoulder in amused bafflement at the mass of figures on the table in front of her, and then shrugged and strolled over to the window. He looked down at the beach.

‘That man is still there, Sophie. Did you see him when you came in? What on earth do you think he wants? He's looking at me now. He's a fierce one, isn't he? I can almost feel the energy coming off him. It's quite astonishing.'

‘Is he?' replied Sophie with little apparent interest, not looking up as her quill hurtled across yet another page of calculations.

Hume's shrewd features showed that he was now in little doubt that there was more to the man's presence than Sophie would care to have him know.

‘You look as if you have been worrying over our little puzzle for some time, Sophie. What are you at?'

Sophie put the quill down at last, and a tiny flicker of self-satisfaction flashed across her face.

‘I'm looking for the strategy for a successful life,' she said with a laugh, ‘and I can tell you that it's no small matter!'

‘How interesting that sounds, Sophie. What do you mean?'

Sophie yawned, suddenly tired.

‘I've been exploring different approaches to playing the Prisoner's Dilemma,' she said, rubbing her eyes. ‘I've been looking at the many possible outcomes that arise from playing both sides of the game and I'm trying to find the optimal strategy for getting the most points by playing it repeatedly. You don't actually need two players to explore the theory, it can be done mathematically. In other words I'm doing what Lord Dunbeath suggested you should do originally when he first wrote to you in Edinburgh. I'm looking for a mathematical solution. You see, those stories we were amusing ourselves with yesterday set me
thinking. If a good society is one in which people lead trusting, productive lives – in other words high scoring games with a large number of partners – then there must be a strategy or an approach that achieves this.

‘But the Prisoner's Dilemma can only be a start point in this process. It's like a stone in this castle. A building block. Of course it tells us what the castle's made of and other things like its colour and hardness – but it doesn't tell us what the castle itself is actually going to look like.

‘So while it's fairly easy to agree that good societies are like games in which people are constantly getting three points, it's also easy to see that others can take advantage of this situation by defecting, by behaving like a free rider and grabbing five at the society's expense. The questions I put to myself were these: how do you deal with these people, these defectors? Is there a strategy to discourage them from acting in this way and instead encourage them to co-operate? And how do you find it?'

She waved her hand over the mass of mathematical workings on the table.

‘The alternative is obvious – an unproductive society in which nobody trusts his neighbour. In which everyone is defecting and only ever getting one point. I think of this as being a bit like a forest. All the energy of the trees is spent in growing higher than the others in the search for light and air. If they'd only stop competing in this way and agree to all be shorter then they could expand their branches and live longer, easier lives. You will never see a tree in a forest that grows as large or as strong as a tree on its own in a field. A society made up of defectors follows the analogy – it's an exhausting, short-lived place where there's no trust and no long term thinking.

‘But what I've been trying to find is whether a co-operator could ever induce a defector to co-operate? For him to become educated in trust in other words. Could a defector, for example, be punished and given another chance? '

She smiled at last as she looked at Hume's kindly expression. He raised a questioning eyebrow.

‘And, yes, I think they can, Mr Hume. I suddenly saw that where the Dilemma departs from the reality of life was that it's very rare that we deal with each other simultaneously. In fact we try and avoid it. We generally react
sequentially
, one after another. The way we communicate when we talk to one another, or write letters, or even when we look at each other, is almost invariably sequential. What we're almost always trying to do, even though we may not be aware of it, is see what the other person is doing and saying before we respond. Or commit ourselves. Unknown to us, we are doing actively what the small boys were made to do passively with their cake. What was it Lord Dunbeath said about that? Didn't he say that each child was making a choice knowing that the other child would be making a choice too?

‘And then I saw that the key to success was based on this observation and I applied the simple principle that
the right thing to do depends upon what the other person does.'

She stopped and laughed at herself.

‘It suddenly occurred to me that if there's no finite end to the game – in other words it's
not
like Lord Dunbeath's one-time Prisoner's Dilemma – then one should do unto others as they have done unto you. Yes, I know, Mr Hume, it's not quite what Aristotle, Plato and all the ancient religions have instructed us. They all tell us to do unto others as you would have them do unto you. And, of course, that should be the approach when one meets a new player. Nonetheless, I rather suspect that the survival instinct in us would prefer to know what the other person is doing first!'

She laughed again, encouraged by Hume's obvious fascination.

‘In other words, it's the very opposite of the lack of communication that the prisoners had in their cells or you had to contend with when you were made to sit behind the book barrier.'

‘So, what do you think the implications of this thinking are for the Dilemma, Sophie?' asked Hume, now intrigued to see if her conclusions fitted with his earlier insight. ‘Did you actually arrive at a strategy that would do this?'

Sophie waved her hand over the reams of workings.

‘Well, I've tried many different approaches but it's only when you've played enough hands over a long period of time that the strengths and weaknesses of different strategies begin to show up. I've been playing against myself for hours, trying everything from ironclad discipline to a mixture of the prescribed and the random. But, yes, I do believe that I'm making progress. I wondered early on if the simple choice of always co-operating would not bring the most points – in the way that the saintly hope they will bring round the wrongdoer. But I came to the view that once selfish people see that they can defect with these committed co-operators without any loss to their own points then the temptation to take advantage of their good natures would be too great for opportunists to resist. Then, for a time I had great hopes for the tactic of simply repeating the same choice if one won but changing it if one lost. It produced promising results for a time but then began to disappoint. However, I persisted with the underlying aim of following one's opponent's choice, and yes, there is indeed one strategy that keeps winning.'

‘How very interesting Sophie,' said Hume, now completely captivated, ‘what is it?'

‘ Well, I think of it as Tit for Tat,' she replied, ‘and it works by simply repeating the choice of the other person. So, when the other person defects I play ‘defect' next. When he co-operates I do the same. It seems to me that it wouldn't take long for him to realise what's happening. In fact the whole point of the Tit for Tat strategy is that it shouldn't be a secret. You actually want the other person to know what you're doing.

‘And it turns out to be a very powerful way of playing, just
because it's so transparent – it's so easy for your opponent to understand. Its strength comes from an irresistible combination of trust, retaliation, forgiveness and clarity. By ‘trust' I mean that the other person can trust you to play co-operate if he does. If he doesn't – and instead plays defect – then he knows that you will immediately retaliate. And this discourages him from persisting whenever defection is tried. The reason is obvious – why would he want to get just one point when he can see that three are available?

‘Once he stops playing defect and goes back to co-operate you restore co-operate as well, so it's a kind of immediate forgiveness. And the strategy's clarity makes it intelligible to the other player, because what you're doing is so evident – and it therefore achieves long term co-operation.'

‘But Sophie,' said Hume, excitedly, ‘did no other strategy achieve the same end?'

‘No.' Sophie shook her head. ‘At first, of course, the nasty, defector strategies kept winning at the expense of the naïve, co-operative players. Only retaliator strategies like Tit for Tat where you have a co-operator who will immediately switch to defect if the other person defects, were able to resist them. But gradually the nasty approaches ran out of the easy pickings of killing co-operators and then defectors kept meeting each other – and obviously their numbers began to decline. This is really the key point. If the defectors kill the co-operators then they're left having to deal with each other! They then dwindle because they kill each other. This was when one sees the success of the Tit for Tat strategy because its retaliation mechanism eventually takes command of the game. Do you see now why I say that there must be a way of playing that educates defectors and rewards co-operators?

‘The way it works shows itself over time – it may lose or draw each battle, but it wins the war. It ensures that most of its games are high scoring encounters and so it constantly brings home the
most points. The crucial insight about the Tit for Tat strategy is that it isn't trying to ‘beat' its opponent – success need not be at the price of someone's failure. A nil sum game is the last thing you want. Tit for Tat is an agreement not a contest.'

* * * 

It was now mid morning and Zweig was in agony, his muscles screaming at their continued contraction. For a bad few minutes he hadn't even known whether he could continue. Then he summoned up a vision of Sophie and yet again he demanded a further effort from his tortured body. He knew there was no going back now, that this was a fight to the end and that his whole being would never allow himself to fail. He leant forward once more, forcing himself to focus his pain on the image of Dunbeath's sneering face that day on the dunes. Slowly his mind conquered the shrieking muscles and again he settled down for the battle with himself that he knew would have to be won.