The Prisoner's Dilemma

by Sean Stuart O'Connor

  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 th
ough. 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.

  ‘But, more importantly than that,’ Hume’s voice now rose in emphasis, ‘we have our histories, we have our backgrounds, we have our reputations. We become known for how we’ve behaved in the past. People already know what to expect from us. They know already whether we’ve shown ourselves to be co-operators or defectors. And whether we’re likely to be so again.

  ‘You see, the Dilemma resides in the prisoner having only two options in his choices. To co-operate or to defect. But this is where the game departs from reality – because in truth a person cannot make a good decision until he knows the choice of the other player. Rather like your little boys and their cake, Dunbeath.

  ‘So, having given the Dilemma a certain amount of further thought, I believe that the key to making this game an insight into our real lives must be to repeat it. But, openly. To keep meeting the same person and to have the potential to reward or punish him for his actions. In other words, to deal with him. There can be no dealing in a one-time game where the risk of error is death. But in reality, in daily life, the stakes are seldom so high, nor is the decision so final. So, instead of having a metaphorical book barrier the opposite is actually true in life – we actively show people what we’re like. If you keep playing the Dilemma in an open way then the game changes and you realise that it pays to co-operate and rational to trust – because you can expect a reasonable opponent to co-operate in return.’

  Sophie had been listening carefully to Hume and she now pulled up a chair to sit by the two men.

  ‘Of course,’ she said excitedly, ‘you must be right, Mr Hume. The interests of the prisoners in the game were completely opposed. But in fact, even then, they would have known each other, and on that basis they might have made a different choice.’

  ‘No, you’re not thinking deeply enough, Miss Kant’ interrupted Dunbeath sharply, ‘because however much you think you may know your opponent, if there’s the possibility of the other person defecting, then you’re better off defecting too. That way you’ll always get one point rather than potentially getting none. And of course you stop the other man from ever getting five. But if your opponent co-operates you are still better off defecting because you’ll get five points instead of three. Whatever the other person does, you are better off defecting.’

  Sophie thought for a moment while she considered this.

  ‘Yes, but perhaps we should not use the word ‘opponent’. It immediately implies conflict and defection. You see, if each person argued in the way you just have, you’ll never achieve anything but one point each – when you could have had three each if you’d only co-operated.’

  As she said this David Hume began laughing, his normal easy humour completely restored.

  ‘Well,’ he said quickly, ‘if you imagine two people playing a hundred times and think forward to the outcomes, the range of possibilities must be from one player getting 500 points for always defecting while the other would end up with none for constantly choosing to co-operate. But the other person is bound to defect once he sees that there’s no point in co-operating. Neither extreme is feasible. Both people co-operating, on the other hand, would lead to 600 points for the pair and a very easy relationship that would be.

  ‘But one can see very quickly how tempting it would be if the other person was always co-operating to slip in the occasional defection just when the other player is lulled into thinking that there would never be any change. Five additional points while the other gets none. Yes, very tempting indeed. Imagine, for example, one of our thieves hiding from the captain of the guard. He’s been given sanctuary in a monastery where the monks treat him with trust and kindness. How long would it take for him to rob them? To grab five points for defecting while the poor monks would get none for their troubles?’

  Dunbeath smiled.

  ‘Exactly,’ he said.

  ‘But what seems to be clear to me,’ Hume continued, ignoring Dunbeath’s pointed comment, ‘is that when we find people we like and want to deal with, the game changes. It stops being a dilemma. What begins as irrational behaviour in trusting the other person – to think of the outcome for both people rather than just for themselves – becomes a rational decision in the long run, as long as there is a long run, as both players ought to co-operate.

  ‘In any case, perfect rationality must be a fiction. To expect it is, if I may say so, to despise your fellow man so much that you withdraw from his company.’

  ‘I presume you are referring to me?’ said Dunbeath. But he didn’t seem displeased by Hume’s remark.

  ‘But it’s interesting, is it not,’ continued Hume without being drawn to answer Dunbeath, ‘that in the animal world the most robust of the species also seem to be the ones that are the most co-operative. And, shouldn’t man, with what my friend Adam Smith calls his ‘specialisations’, be even more open to the benefits of co-operation.

  ‘So, is selfishness an animal instinct, and trust – for surely that is what co-operation must be – a civilised one? Are the most successful animal species the ones that are continually attacking each other or those that show the greatest mutual support? I think you’d agree that most observations would point to the latter. Indeed, their world is so often a lesson to us. Everywhere one looks one sees co-operation even to the point of sacrifice. Does not a bird call out to its flock when it sees a cat – even though it gives its
own position away? And look at so many of them when they are together. Particularly the more dangerous species. See in what a ritualised way they behave – twisting and retreating, sudden rushes and snapping. But mainly glowers and feints and noise. How interesting, though, that they very rarely do each other real harm.

  ‘So what might this mean? Well, I think the start point has to be that if we’re alive at all then we have to be examples of some kind of successful strategy. The only certainty in life is that our ancestors didn’t die celibate. Perhaps the behaviour they employed to enhance our survival was thriving at the expense of the behaviour that failed for other people? This sole fact alone points to us being the living proof of some kind of winning approach. We humans may think that we are subtly individual but really we are just machines bent on survival. What is it that’s making us behave instinctively in the way that we do?’

  Hume leant back in his chair and picked up his wine again. Dunbeath was so pleased with Hume’s observations that he was now smiling.

  ‘I am in your debt, Mr Hume,’ he said, ‘you nursed me back to life and now you are making me think. I believe I profoundly disagree with your conclusions but I very much look forward to continuing our game.’

  Hume set his glass down.

  ‘Well, I’m delighted to hear that, my lord. I shall greatly enjoy doing so. By the way,’ he continued, ‘what was it that you witnessed that made you think of the game in the first place?’

  ‘What’s that, what do you mean, Hume? Dunbeath said with an abruptly renewed sharpness, ‘I’ve no idea what you can be referring to.’