The Prisoner's Dilemma (19 page)

The following morning Sophie rose early and went immediately to her bedroom window. She'd blown out the candle the previous evening and waited a minute before creeping over to arrange the curtains so she could see Zweig through a slight separation in the folds. But, as she looked out now, her heart sank as she saw that he was still there. And still staring at her. She was beginning to panic, astonished that he could know that she was at the window. Then she rallied, telling herself that he couldn't, that the glass must be completely black from the outside, that she must just carry on. She resolved once again to say nothing of this to Dunbeath. The madman was bound to give up soon.

She dressed and went down to the earl's study. She had woken in the night, anxious that an error might have crept into the nutation values of the ecliptic in her calculations and she now unravelled the presentation papers they'd prepared for the Board and set to work on yet a further check. After about half an hour she concluded that all was well but as she got to her feet she felt herself being pulled, once again, to the window. She stood well back from it so that she couldn't be seen. How did he do it, she brooded, watching Zweig as he carefully studied the castle for any sign of motion? He seemed as alert now as when he'd started.

As she stared down at him she was only too aware of the mass of conflicting feelings that were rising up in her. Distrust and disdain certainly; and yet unquestionably, admiration and concern as well. Above all, she was nagged by a great uncertainty – was the man motivated only by his greed to recover her father's debt? Or was he really driven by the love that he'd told her of when they were on the ship? He'd said that day, and then again on the dunes, that he would never leave her. Would he really put himself through this extraordinary ordeal simply for money? Or was he trying to show her his true feelings?

She looked at him more closely and saw the simple
fisherman's clothes he now wore. He looked somehow more sincere in them. There was less ostentation, less pretence.

She was so deep in her thoughts that she didn't hear Dunbeath as he came into the room behind her. He began to speak and she jumped at the sound of his voice.

‘What do you think he wants, Sophie?' the earl said quietly, walking over to the window and then gazing down at where Zweig sat. ‘What compulsion do you think is driving him? This is the third day your captain has been here, lined up in full view of the castle like a besieging army, calling us out to battle. You speak of co-operation but see for yourself what a man will put himself through for his own ends. I dare say he would like to tell us what game he's playing but I think we hold the better hand, because we do not wish to play with him at all.'

He turned away from the window and looked at the papers that Sophie had laid out neatly on his desk.

‘Ah, Sophie, I see that you have been testing the logic of the presentation yet again. I have done so myself so often that I have to believe it now rings true. As far as I can tell the charts are all in order for when we shall see the Board of Longitude. Everything appears to be ready for them - but you will still come with me when I go to London, won't you?'

‘Yes, of course. I look forward to going. It will give me a rest from the Prisoner's Dilemma.'

Dunbeath turned to gaze at her, his expression struck by a mixture of regard for her mind and an almost childlike adoration for her personality.

‘That odd child of mine, the Dilemma. Yes, I'm so sorry I wasn't there when you were explaining your findings yesterday. Hume has told me about the success of your Tit for Tat stratagem. It's very clever. It seems so simple – and yet you say that it constantly beats other ways of getting the most points.'

‘Yes,' said Sophie eagerly, only too happy to move away from the window and distract Dunbeath from looking at Zweig – and
also from the thoughts that were clouding her own mind, ‘if by that you mean over a long period of time and in willing and repetitive relationships, then yes. In other words it apes the reality of life. The irony of its success is that a player that would have been described as irrational in your original one-time Prisoner's Dilemma, by trusting his partner to stay silent, is now seen to be rational. He is the calculating one, choosing partners to build high scoring relationships with and punishing those who abuse his trust.'

‘But Sophie,' said Dunbeath, becoming suddenly testy at yet another assault on his own conclusions to the Dilemma, ‘haven't you now introduced the idea of personality into the game? When we first played it we were at pains to agree that the players had no moral code. Rather they were utterly competitive, with no room for sentiment.'

Sophie looked at him with the gentle care of someone calming an invalid.

‘I have to agree that the process began in that way – that only logic should prevail in looking at our instinct for survival. But if one accepts that the true insight from the game comes from seeing it played repeatedly and sequentially, then it's obvious that judging who one can trust is the key skill in telling whether other people are defectors or co-operators. After all, the only way of finding out if you can trust someone – is to trust them!'

‘And this skill of yours, Sophie, how do we develop that?' Dunbeath was drawling his words now with more than an echo of the arrogant and cynical tone he had first used with her.

‘I don't know that we do,' she replied, ‘I think instead that the need for trust, just like the need for exchange or barter in society, has become woven into our natures. It's an instinct. But why should we think this is so odd? Why do we think that instincts are only animal impulses? Most animals know instinctively from birth how to walk, to eat, to fly even. We, on the other hand, spend years being unable to survive without the constant
attention of others; we spend months as just tiny babies, and then years as children, capable of nothing without being cared for. This vulnerability must have left us with other gifts. I would suggest that one of them is that we can sum each other up in the blink of an eye.

‘I believe we know instinctively who we think we can trust. Who might help us. We don't need to stumble along until we come to the conclusion that ‘one good turn deserves another'. Nor do we need to be taught this. We are not shown it any more than an animal might be shown how to stand or to walk. It is an instinct, and this instinctive knowledge must come somehow from our ancestors – and our continued existence is evidence of their success.'

‘Oh really, Sophie,' said Dunbeath, clearly becoming irritated, ‘this talk of trust bewilders me. My experience is that hoping for trust in others is nothing but a fool's idea of paradise. On the contrary, my maxim is not unlike the Urquhain motto. Trust nobody - and you won't be disappointed. I mean to say, how does your Tit for Tat idea deal with people who would break your trust in them? When your instincts prove to be wrong.'

‘But that is its strength,' replied Sophie. ‘The mechanism works even if one makes an error in trusting someone. Tit for Tat shows that we can turn our back on a defector. Most people learn quickly that even the occasional mistake can't obscure the lesson that the gains they can make are worth the risk of trusting people in the search to find co-operative partners. That must be why, when one plays these repeated versions of the Dilemma, it is the ‘shadow of the future' that's deciding the outcome.

‘In my view these games of ours show up the key principle that the right thing to do depends on what other people do. It's a simplified insight into how the world works. You see, while the only thing to do in your original version of the Prisoner's Dilemma is not to trust the other person, because you don't know what he will do, Tit for Tat shows us that an approach that tries
to co-operate with people can succeed
when the Dilemma is openly repeated
. The strength of Tit for Tat is that it doesn't envy or want to beat its opponent. It wants a fair share of a growing whole, not to be fighting over a smaller pot. The image comes to me of a primitive man killing someone for an old bone when he should have been working together with him to hunt for more game.

‘I really am convinced now that humans have evolved an understanding that trust wins because it leads to co-operation. And that an ability to judge who you can trust is a crucial skill in life. Where did this come from? Perhaps a great change came over the way we viewed each other about the time that hunters gave way to farmers? People must have realised that co-operation meant bigger harvests. Life was more secure. After all, your neighbour couldn't steal a field of wheat in the way that he could take a deer or a rabbit you'd just hunted for the pot.'

As she spoke Dunbeath had begun moving from foot to foot, irritated by her conviction on the mechanism for co-operation, yet determined not to lose his self-control.

‘And what are your conclusions to all this, Sophie?' he now managed to say in a fairly even tone.

‘Well, I think that at base this instinct has made us very clever, cleverer than we know. You see, unlike these games we are not simply playing in response to what the other person actually does. We're going further than that. We're
interpreting
our opponents' thoughts and actions as well, and each of us is behaving on the basis of what they think the other will do – imagining and concluding on how the ‘shadow of the future' would affect other people's next steps.'

But this had finally gone too far for Dunbeath and he began to show signs of his old arrogance as he listened to Sophie's insistence on the natural place of goodness. He was far too cynical and wedded to his sense of superiority to understand such a counsel of sharing.

‘Now, let me understand you, Sophie,' he said slowly, and
with more than a trace of harshness in his voice. ‘You say that if you found a partner, a co-operator, someone you felt you could completely trust, you would never cheat on them. That you would never tire of getting three points. You say you'd never take advantage of your partner's trustworthiness and be tempted to slip a defection in. Is that right? After all, you'd be rejecting the opportunity to get five points and seeing to it that they got none. You'd win the game easily over the long run if you did that, wouldn't you?'

‘No, I would never do that,' Sophie replied slowly. She'd heard his tone and wondered what trap he was setting for her now.

‘Then let me ask you this,' continued Dunbeath, ‘if I gave you £100 and told you to split it with Annie, what would you do?'

‘I'd give her half.'

‘And why would you do that? After all, if you gave her £10 she would still be delighted. It would be £10 she didn't have before – a great deal of money to her. And you would have £90. No doubt £90 would be welcome, should you want to return home to Königsberg.'

Sophie was shocked when he said this. She had never asked the earl for money and yet he had guessed her mind. She now drew herself up to give greater emphasis to her answer.

‘No, I couldn't do that. It wouldn't be fair. It wouldn't be right.'

‘I see, so the reason you wouldn't do it is because of your wish to be seen by her to be dealing fairly. But if you could see that she got some of the money and I could
guarantee
that she would never find out where it came from. It would be a complete secret. How much would you give her then?'

Sophie went quiet. Dunbeath smiled and gently leant towards her in a little show of triumph.

‘Exactly. Your hesitation shows you are human after all. You will agree with me then that the issue is one of reputation and
not one of integrity. Of not wanting the other person to know that you haven't shared equally. If it were a secret from her how the money was divided then you would think differently. In other words the way you'd behave reflects your view of the future – your concern to be seen as fair in Annie's eyes – rather than your instinct for survival. And a passage to Prussia.'

There was a silence as Sophie considered Dunbeath's questioning. She felt annoyed with herself that he had led her so easily into admitting such a very human weakness, such a secret instinct for gain - even such a longing to go home - but her nature was too honest for her to have pretended otherwise.

Dunbeath looked down at the floor and then quietly continued. He had been waiting for just such an opportunity to press his advantage.

‘Now Sophie, I must ask you about that ship's captain of yours. He is still sitting on the dunes. It's been two nights already and now we have a further day, and he still shows no sign of weakening. A remarkable performance I grant you. But what is driving him? Nobody would last this long without a madness to prevail, to win even. I feel you owe it to me to say what this is about. What is it that he's after?'

With a sigh Sophie realised that she could remain silent no longer. And so she took Dunbeath back to Königsberg and told him of her life there. She described Zweig's great rise amongst the merchants and the shipping powers and then she recounted the story of her father's disastrous loss and the debt this had led to with Zweig. Dunbeath listened intently, occasionally putting questions to her and then asking how, sad though her father's miscalculation had been, this situation could have ever involved her. She sighed again and painfully told him of how she had come on the voyage as a hostage for the money her father had to find. She finished by saying that the debt would be annulled if the two of them did not return within a hundred days of their departure.

But, crucially, she omitted to tell Dunbeath about Zweig's wish to marry her. And her suspicion that his love for her was making him risk everything as he sat outside, demanding to be dealt with. Instead, she finished by saying that she lived with her heart in her mouth, counting the days until her father's position was safe.

‘And how many are left?' asked Dunbeath intently.