The Prisoner's Dilemma

by Sean Stuart O'Connor

  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.

  Chapter 14

  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 expr
ession. 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!’