The Prisoner's Dilemma (15 page)

‘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.

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.'

An unpleasant edge had come into Dunbeath's tone, a kind of triumphant bitterness.

‘You've had your chance to defect as well, Mr Hume, indeed many chances, but you've chosen instead to act irrationally, imagining that your benevolence can get an opponent to co-operate. Have you not concluded from the game that when you
choose ‘co-operation' and I choose ‘defect' then you get nothing? Really, are you such a fool as not to see that whilst the prisoner may perceive a dilemma a rational man would not. Can you not see that?'

As Hume listened to Dunbeath's hectoring tone and the harsh words he was spitting out, a horrible, cold realisation began to sweep over him – a realisation that the earl hadn't brought him to Caithness to play this game with him at all. That he'd foreseen all this. That he'd got him to come so he could crush him with this unpleasant little drama. Hume began to think of why he'd done this. He imagined Dunbeath becoming aware of his own small amount of success in Edinburgh, and of how a man like the earl couldn't bear to think of an old acquaintance outstripping him, or for him to allow even a modicum of fame in someone he'd consider well below him, below an Urquhain. In an instant Hume could see the years Dunbeath had spent at the castle, miles from anywhere, buried under the weight of his research, getting no recognition at all – and knowing with an utter conviction, even if he'd be the only one that did, that he was superior to such a trivial person as a mere thinker. How that must have eaten at him! How much he would have felt the need to put him in his place.

As David Hume came to the end of his frantic musing he saw that the light in Dunbeath's eye was rapidly becoming a fire.

‘Yes,' Dunbeath repeated for the second time, ‘can you not see that? I've read your work, Hume, that
Treatise
of yours. I've read that nonsense you spout about benevolence and trust. But I have proved beyond argument, have I not, that this is a strategy for failure. In this world it is the strong that realise this. That is what the Prisoner's Dilemma shows.'

His face was now quite twisted in his anger.

‘How do you think the Urquhain rose from this piece of useless wasteland, from just a patch of rock and sea, to where we are now? How have we climbed? Believe me, because I know it
to be true, we are the richest family in Scotland. And, how do you think we've done that? It's because we've been playing this game for centuries. We know how to win. Put that in your next book, Hume, accept that the world is for the powerful and have done with it!'

Hume's face was puce with the unfairness of the attack. In friendship and interest he had made the trek to Caithness and now this madness was breaking out about his head. His hand crept yet again to stroke his cuff but even this no longer had the power to calm him. By now the two men were on their feet.

Over by the fire, Sophie had been quietly listening as the games had been played. She now looked over with alarm as their angry voices filled the room.

‘I cannot remember ever being so ill treated, Dunbeath,' said Hume, struggling to keep his tone even. Like all men of a naturally even temperament he was bewildered and hurt in the face of injustice. ‘I will not endure this. That you have brought me all the way from Edinburgh just to waste my time with your theories and then to rub my nose in this selfishness – this ‘proof' that selfishness wins. Really, Dunbeath, are you so angry with the world that you would trick me into coming here, just so you could make your point?'

By now Hume was fighting to keep his temper and he made to take a step towards the door.

‘I bid you goodbye, Dunbeath. I'd thank you if your housekeeper would arrange for a trap to take me to Wick.'

Dunbeath didn't answer and the two of them remained facing each other, both rigid with fury. Neither had noticed that Sophie had walked across from the fireplace. She was now between them.

‘Surely,
that
is the point?' she said calmly.

Both men looked at her intently, their concentration broken for the first time by her presence.

‘Surely,' she repeated, ‘the point is that Mr Hume has decided
not to continue the game. He has decided that you, my lord, will always defect and he sees no future in continuing to play with you. He is, in other words, behaving in exactly the way that a reasonable, co-operative person does when faced with such intransigent selfishness – he has decided to avoid you.'

There was a stunned pause and Dunbeath's face began to work with instinctive anger at being so criticised, so crossed. But, as he looked at her in his rage, his features softened just as quickly as they had set. And, to Sophie and Hume's amazement, he gave a quick laugh. Then he appeared to smile at his own change of mood and he turned to her, almost affectionately.

‘Only you, Sophie, could have said that to me. And only since my illness.'

He strode over to the curved window and brought back a decanter of whisky.

‘A peace offering, Mr Hume. A dram with me for our friendship. It is only when one has known someone as long as we have that we do not take offence. Is that not so? A glass with you, Hume. I trust you will reconsider your wish to leave. We still have much to explore with this game.'

He raised his large crystal rummer in a sign of regard and drained the whisky. Hume raised his own in return but saw that Dunbeath's mood had changed again now that he'd considered that the discussion had come to an end.

‘I must away to my study,' he said briskly. ‘Sophie, perhaps you would join me there? As you know I am much troubled by these lunar distance errors that I can find no cause for. Do you really believe they are time dependent? Your knowledge of the orbits of Jupiter's moons may help to explain them – they are the universal timekeeper. Perhaps you could share von Schleimann's formula with me?'

‘Yes, indeed,' she replied, still astonished by the extraordinary journey of his mood, ‘there is much still to cover. I shall come in a few minutes – just as soon as I have finished here.'

* * * 

Zweig had walked around the headland and was now working his way down a low cliff to the foreshore, where the surf met a line of jagged rocks. He looked intently into the pools the retreating sea had left, apparently searching for something.

After half an hour he seemed to find what he was hoping for and he leant down to pick it up. It was a strong, straight piece of broken tree branch, sodden and heavy with seawater. He felt its weight in his hand and then went to sit on a nearby boulder.

Reaching inside his jacket he took a sharp gutting knife from his pocket and began to whittle the sides of the stick, shaping it into an even cylinder.

* * * 

‘Are you not joining Lord Dunbeath, Miss Kant?' said Hume once they were alone.

‘I shall do so in a short while, Mr Hume, but I would appreciate it if I might ask you a question first.'

She looked at Hume's gentle features with concern.

‘I fear I do not understand his lordship at all. Why does he think there is a need for such anger? You know him well yet you feel able to forgive his attack.'

‘Dunbeath? Oh, he is not a bad soul, Miss Kant. No, not at all. I think we both know that. You have to look beyond the man you see standing before you. You have to see four hundred years of a family's relentless need to succeed. An unbroken chain of duty that stretches over the generations – win, win and never leave off winning is all they ever think of. Enough is never enough, others must fail. And all this fire and ambition ends in him. The Urquhain are not alone in this mania, Miss Kant, I have seen it in other clans and families as well. Far from being dismayed by Dunbeath, I pity him. He has only ever known the separation
from other people that comes with superiority, endless duty, competition, and the constant need to keep his inferiors down. He's never felt any affection or ever been allowed it. And yet I believe he yearns for it more than any man I know.'

‘You may be right, Mr Hume,' said Sophie, turning to look at the flames in the great fireplace, ‘I had not seen him with the clarity you have. I admire you for your forbearance though. He is not an easy friend.'

* * * 

Later that evening Hume and Dunbeath made further amends to their old relationship as they sat opposite one another at the long dining room table. Sophie came in holding a plate loaded with yet more dividends from Annie's expedition to Wick and David Hume glanced up at her over his wineglass, now far happier with the world – and with Dunbeath.

‘Ah, Miss Kant. More food eh? You and Annie are too kind, too kind'

He paused, uncertain of how he would best express a sincere regret.

‘But while you are here,' he continued, ‘I would like to apologise for becoming so exercised with Lord Dunbeath this afternoon. I have said as much to him myself. I am indeed glad that I did not set off back to Edinburgh. I would have missed this fine dinner. But since we parted then I have also given the Dilemma a deal of thought. And I have concluded that my old friend was correct in his views.'

Sophie set the dish down in surprise as Hume pressed on.

‘Yes, I have reflected and now see that there is only one possible conclusion. I have come to realise that when two completely rational, mutually competitive, cold hearted people have a ‘one time' game like the Prisoner's Dilemma –
and are set only on winning at that time
– that indeed there can be only one
outcome. Lord Dunbeath must be right. The only rational way to proceed in such a game is to defect.

‘In fact,' continued Hume, ‘when you have two clear thinking players who have set any notion of friendship or trust to one side and whose interests are completely opposed, I can see no alternative but that a state of equilibrium arises very quickly from which neither player would
ever
be able to change their choices – however much it might improve their positions if they did so. And no doubt their lives.'

‘I believe you are describing many a marriage,' laughed Dunbeath, his own anger now completely dissipated by Hume engaging with his concept and allowing him his victory.

Hume laughed in reply, but then held up a forefinger. He was now completely serious.

‘However. Life is more complicated than that. The way we played the game this afternoon is unrealistic. In the Prisoner's Dilemma there was no communication – you'll remember that the prisoners were in separate cells and you tried to replicate that with your book barrier – whereas in life there is. In fact, this is very much the point because in reality we
do
communicate with each other, we give off clues about ourselves all the time and project a thousand and one seen and unseen signals about what we're thinking. You said as much yourself, Dunbeath, when you explained your game. All that bluffing and feints and deceits you spoke about then.