The Prisoner's Dilemma

by Sean Stuart O'Connor

  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 susp
ected 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.

  ‘And then let’s agree that both confessing and getting a lesser sentence is lower than this but obviously better than being the only culprit. Make that one point. Is that clear?’

  ‘I think so,’ said Hume brightly. ‘The four outcomes are worth five, three, one and no points. Yes, I think that’s the right reflection of the possibilities. So, if two people take the obvious route of co-operating then they’d get six points between them – two threes – rather than someone getting the maximum score of five for betraying a colleague. I like that. Trust is rewarded over selfishness. But I’m still not sure how we proceed.’

  Dunbeath pointed to the table in the alcove.

  ‘Good. I’m glad you agree to the principle. Then come over here and we’ll play a few hands.’

  Saying this, Dunbeath walked Hume to the table and showed him how he had piled up books to make a high dividing wall in the middle of its surface. He gestured to Hume to sit on one side of the books and he went to the other. He showed him that each side had some sheaves of plain paper and a quill and ink alongside them. They then sat down and made sure that they couldn’t see each other, nor what they were writing.

  ‘So, game one,’ called out Dunbeath. ‘Write down if you would stay silent – in other words co-operate, trust the other person – or whether you would confess. I call a confession Defect because you would be defecting from trusting your colleague. If you want to co-operate write ‘C’ and if you wish to defect, write ‘D’. We can’t see or hear each other so it’s just as if we are in separate cells. In fact, to make things absolutely safe, don’t do the down stroke on the ‘D’, just make a reverse ‘C’. That way neither of us will ever be able to guess from the scratch of the quill what the other is doing. Very well, the first play, make your decision.’

  They both wrote a letter.

  ‘I’ve written ‘C’ said Hume, looking around the book wall. ‘I chose to co-operate. No doubt you did the same.’

  ‘No, I have written a ‘D’. I defected,’ replied Dunbeath. ‘Five points to me and none to you.

  ‘Now, game two.’

  They began to write.

  Chapter 12

  Zweig slowly padded in his strange, deliberate way along the foreshore, his head down, deep in thought. He had now lost everything. For a time he had felt he’d held a card by having the telescope, but Dunbeath had seen to it that even that had been lost – and with it, much worse, the hold he had over James. There was now the great danger of being exposed to the English by that weak-minded, murderous boy. There was no longer anything in his hand.

  He stopped by the water’s edge and looked out to where the surf broke over the rocks that had seen the end of his ship. But there was no sign of self-pity or defeat in his face, only a trance of concentration. For ten minutes or more he barely moved, his thoughts progressing with all the discipline of a regiment of guards as he carefully relived recent events in his mind, seeing the people involved, weighing them up, listing their strengths and weaknesses. Imperceptibly, he seemed to swell as if he was absorbing the power of the sea, reaching deeper and deeper into himself, marshalling his resources and planning his next steps, seeing his options, plotting his moves.

  Eventually he lifted his head and gave a minute nod as if to confirm his conclusions to himself. His mind was plainly made and there was a renewed determination in his face as he turned
and began the walk back to Dunbeaton, now with a quite different substance to his tread.

  * * *

  It was early evening and the candles were throwing their mad, twitching light about the plasterwork of the great salon.

  ‘And I defect again,’ said Dunbeath with more than a slight note of provocation in his voice.

  Hume’s fabled equanimity was wearing thin. His hand strayed yet again to the embroidery at his coat cuff.

  ‘I estimate from my notes, Dunbeath,’ he said with a terse edge to his voice, ‘that we must have played this game of yours a further five blocks of ten times this hour. And all you have done is repeat your choice. On every occasion you have chosen to defect. I cannot see the point you are making.’

  Dunbeath’s face had returned to the look of blank disdain he wore before his illness.

  ‘My point? Surely you can see that I am making my point every time we examine the outcomes we have chosen? I defect. You too could have done so and yet you almost invariably choose instead to co-operate, no doubt in the hope that I can see some kind of benefit from it.’

  ‘Of course I do,’ replied Hume, his voice rising in emphasis, ‘we would both get three points if you would only do the same. When I defect as well you only get one. As do I. Do you not see that co-operation leads to more points? We would get six points between us rather than one each or even the five to you.’

  ‘And do you not see that I have over two hundred points and you have but five,’ said Dunbeath looking down at the score he had been keeping. ‘That is the real point. I am beating you. Is this not enough for you? Do you not see the truth about life here – that it is simply a struggle between self-interested creatures? It is about winning and losing. And this game is the proof of it. Humans may sometimes be tamed by their cultures, or laws or force, but by nothing else – and certainly not by the prospect of your wish for co-operation, by some vague hope of yours that it leads to what you call trust.’