The Prisoner's Dilemma (14 page)

Sophie forced herself to be calm. She slowed her step to even the rhythm of her pace – that would clear her head, she felt. So the madman was still alive! Of course he was. It would take more than a shipwreck to kill him. He was a force of nature, even if the livid scar on his head showed he could bleed like a human. She had forgotten what a colossal man he was, towering over them like that. But how much better he had appeared without his tassels and fur – just simple fisherman's clothes and an old tweed coat.

Thank heaven we spoke in German, she thought to herself. Annie would have followed what we were saying otherwise and understood what all this was about. Luckily Lord Dunbeath had been too far away to hear. She walked on, thinking through what she would say to them about Zweig. They would want to know who he was and what he wanted. She knew she couldn't avoid telling them he was on the ship – Annie would have guessed that anyway – if not, she'd be bound to gossip in Dunbeaton and no doubt the villagers there knew who he was. Yes, it was bound to come out that he was the ship's captain. But why should she hide it anyway? Did it really matter?

She walked a little way further, still deep in her thoughts.

Dunbeath would question her. That look he'd given her when she'd sat by his bed, and then how he'd stared at her before she left for the village. Yes, of course, he would probe. And she'd seen how the two men had looked at each other back on the dunes. Like a pair of rutting stags, sizing each other up. And Zweig had said that thing about making an impression. Yes, Dunbeath would want to know.

She gazed out to sea and felt the freshness of the breeze on her face.

But if they were going to know about Zweig being the captain, why shouldn't she explain about the debt agreement too? There
was no need to speak about the marriage contract. Her being the security on the debt was the explanation – that's why he needed her to go with him. She was sure this was the right approach.

To her astonishment, Dunbeath mentioned not a word when they eventually climbed the long steps to the drive and entered the castle. Was he too lofty to have seen what was going on, she wondered? Too removed in his aristocratic superiority? Or perhaps too locked in the workings of his mind and his ambition to ever acknowledge the squabbles of lesser beings?

Whatever the reason, Dunbeath merely turned and muttered to Annie as they came into the hall.

‘Put the horse in the trap, Annie. Take the road to Wick and provision there. Or buy from the men that bring things to the castle. There's no reason for you ever to be in Dunbeaton. I don't want you going there again.'

He walked up the stairs to the drawing rooms but had only climbed a half dozen steps before he turned back.

‘Before you go, Annie, send my compliments to Mr Hume and ask him if he will meet with me in the great salon at noon. Miss Kant, perhaps you would care to join us there? And, Sophie,' he added, now more quietly and with no little concern in his voice, ‘you may wish to let me know in future if you are leaving the castle.'

Sophie's downcast look showed him her agreement. She turned to walk away, glad of the opportunity to cover her astonishment. Sophie! How would he have known that was her name? He would have heard Hume call her Miss Kant, but how could he have learnt of Sophie? He could only have been speaking to Annie about her. How he would have suffered to have stooped to that. Yes, Zweig was right, she had made an impression. But perhaps God was at work here? After all, the longer that Dunbeath was interested in her, the longer she would be able to stay in the castle, under his protection. That would make certain that Zwieg couldn't somehow force her back to Königsberg. This
had to be the only thing that mattered for the next few weeks – as long as she was safe in Scotland the debt couldn't be called.

Her face tightened in determination once she'd reached her conclusion – she had to stay in the castle for the sake of the debt: that much was clear, yes, that was the only thing that mattered.

* * * 

It wasn't long before Annie had found David Hume and an hour later he and Dunbeath were standing in front of the open fire, glasses of whisky in their hands and an evident sense of promise in the air. Sophie was continuing where she had left off before Dunbeath's collapse, clearing up the years of neglect, restoring the great rooms, rehanging curtains and sorting through the mass of discarded books.

Eventually, Dunbeath's tense features showed that he was about to embark on the most loathsome of obligations for him – an apology.

‘I must plead forgiveness for taking up so much of your time with that damned illness of mine, Mr Hume. I owe you a great debt for your concern for my wellbeing and for being so attentive. You have been most patient. But now, at last, if you are still willing I shall explain the Prisoner's Dilemma to you. And then perhaps we might even play a few hands.'

David Hume's usual good humour was in full blossom as he smiled and waved a dismissive hand.

‘Not at all, Dunbeath. It is behind us and I am glad for your recovery. And at last I am to hear about the mysterious Dilemma! I've been greatly looking forward to this; but I must confess I'm still completely perplexed as to how you can claim that a game can ever give an insight into our natures.'

‘But all life is a game, Hume. What are we doing if we are not constantly dealing with each other, playing a great game, forming alliances, weighing up our options, misleading, trusting,
not trusting, saying what we mean, what we don't mean, shifting our ground, working out our stratagems? Above everything, all of us, all the time, are playing to beat our fellow man.'

Well, I would agree with much of what you say,' replied Hume, ‘but you seem to place great emphasis on winning. Where is fraternity and harmony in your games of life?'

‘Harmony? In humans? Really, Mr Hume, you are too naïve – and I intend to show you why. As to my game, I'm not talking about pastimes like chess where there must be a solution, a right procedure for any position. Real life is not like that. Real life consists of bluffing, of little deceits, of feints, of asking yourself what is the other man going to think I mean to do. That is what games are about in my theory. My interest is in understanding the things we are doing instinctively, a hundred times a day, unknowingly most of the time and always supposing that we are in the right. It is about seeing how we look to gain an advantage and how we solve problems.'

‘Well, again, I shall concede to you on that description of life. But a game?'

‘Yes, because games show us the ways we are trying to win in life. Let me give you an example. A very simple game. You have two squabbling small boys – they will agree on nothing. Now, how do you cut up a cake between them without a fight? When neither would ever agree that it would be divided fairly?'

‘A desperate situation, I grant you,' replied Hume with a light laugh. ‘Small boys would be second only to university professors in their sense of grievance that somebody, somewhere, might have something that they do not. But let me try to give you an answer.'

There was a pause while Hume thought further about the question.

‘I believe I would try to get them to see the shortcomings of ever expecting perfection. I would tell them that there can never be perfection in life. I'd explain that a careful eye and a steady
hand should ensure a clean cut to the cake and that any thought of the crumbs of difference between the two pieces should be ignored. Perhaps a trusted intermediary could be asked to make the cut and then choose who gets which slice? Or perhaps they could toss a coin to see which of them would have first choice? I suppose that would be my message, given in as peace-loving a way as I could deliver.'

‘I disagree with you,' said Dunbeath, with more than a slight air of triumph. ‘I would see the boys as willing competitors in a game. Cunning and potentially deceitful opponents. I would tell them that one can cut the cake and the other can then choose which piece he wants. Each is now responsible for the outcome. Neither can complain. It may be a simple story but it shows you how a contract of greed, a low impulse you would no doubt say, can lead to harmony in a way that persuasion never could. Far from your idealistic ambition for them to be peace loving, one would rely instead on their passionate hostility to each other to find a solution.'

Dunbeath thought for a second and then continued, stretching out a finger for emphasis.

‘One of the boys has to make a choice knowing that the other one would also be making a choice. Each child anticipates what the other child will do. In a similar way, the Prisoner's Dilemma also shows the way we constantly use strategies for dealing with each other.'

Hume chuckled happily.

‘I enjoyed your story. A very elegant solution. So please explain the so-called Dilemma to me. I hope it is as intriguing.'

‘Very well,' Dunbeath nodded. He took a sip of his whisky and considered for a few moments before he began.

‘I want you to imagine that there are two prisoners. They are being held in two separate cells, some distance apart. They certainly can't see or hear each other. They have been picked up together, near a house that has been burgled, and they are
suspected of the robbery. The authorities are quite sure of their guilt but there's no sign of any of the stolen property and they don't have the hard proof they need for a conviction.

‘The captain of the guard visits the prisoners in turn and tells each of them exactly the same thing.

‘He says to them: ‘Listen carefully. We know that you were near the scene of the crime. We also know that you and your companion are thieves. But the fact is that we don't have the watertight evidence to convict you. So, I need you to tell me that you did rob the house. Yes, I want you to admit to the crime.

‘Now, if each of you confesses and pleads guilty then I shall see that the court hears about your honesty and you'll be given lesser sentences.

‘However, if you both remain silent and don't admit to anything then I shall still send you for trial. But, without the evidence I need, you will probably only be convicted of trespass. And for that you would get far less time in jail than you would if you came clean about the theft.

‘But, and pay very careful attention to me here, if you confess to the robbery – and your friend stays silent – then I shall see that he hangs alone for the crime. And you'll be rewarded by being set free.

‘I'll come tomorrow morning at seven o'clock to hear your answer.”

David Hume was very still as he absorbed the drama.

‘Now,' continued Dunbeath, ‘the thieves sit in their cells and think about this. Each of them concludes that the best outcome would be for both of them to stay silent. That way they can only be tried on the minor charge of trespass. But the more they think about it the more each of them has a horror …what if
I
stay silent and
he
doesn't? He'll give evidence against me. I'll hang and he'll go free. What if he doesn't care about me but only thinks about himself? Can I trust him to keep quiet?

‘All night long the prisoners think about this. The terror of the
three o'clock chimes and the blackness of their cells eat at their confidence. And, of course, it's not long before they both come to the same conclusion – the risk is too great. I'll confess. That way I'll go free if my partner stays silent. He would hang but I'd be free. But if he thinks the same way and confesses as well – then we'll both get a lesser sentence anyway. The captain promised that.

‘The captain comes at seven but he's been playing this game for a long time. He already knows what he'll find. Both of them confess.'

‘How interesting,' said Hume softly, ‘how very pretty. Although it would be obvious to each that staying silent would lead to the best result for the two of them – they dare not trust the other to think in the same way. I can see what you're saying. That it would appear rational to confess even though there would be a better result if both were irrational – and had trust in each other. Yes, very pretty indeed. I congratulate you, Lord Dunbeath, you have very neatly summarised the leap of faith that is behind the nature of trust.'

Hume raised his glass and sipped it as he turned the story over in his head.

‘But I fear I must disagree with your conclusion,' he said at last. ‘You would have me believe from this illustration of yours that a lack of faith in a colleague leads to a desirable outcome. I cannot accept this. I'll grant you that you may be right about the defective morals of a pair of thieves, snatching at an advantage to save their miserable skins, terrified in their cells, the darkest hours breaking their human instinct to be honourable – they would behave in this way. But not a thinking, reasonable person. Not someone in this enlightened age'.

Dunbeath said nothing. Hume pondered further.

‘But, I was quite forgetting,' he said after a pause, ‘you said you had invented a game. Presumably you have based it on this tale. How could this questionable parable of yours possibly
become a game?'

‘Oh, but I believe it can,' replied Dunbeath, ‘and more than that I believe it will show you how wrong you are in what you've just said. In fact I believe I shall illustrate that to you in only a few minutes. Let me first suggest that we give each of the possible outcomes a score. Then we can play against each other for an hour or two. That should see us have a considerable collection of games, choices if you like, and we'll see who can assemble the most points.

‘Let me begin by proposing a way of scoring that would reflect you confessing but the other person staying silent. You get five points for going free but he gets none, no points, as he is the only one that's convicted. In fact he's been hanged, he's dead, so no points at all. The average of these scores is two and a half, so let's make the reward for
both
staying silent more than this. Say it's three.