The Prisoner's Dilemma

by Sean Stuart O'Connor

  ‘But there’s more than that.’

  He laughed as he pulled out some further sheets of paper from his valise.

  ‘Yes, much more, Mr Hume. In fact, what I have here is your own testimony, clear as daylight and ready for your signature. I rather think that this would carry the day.’

  ‘What! What are you talking about now, L’Arquen?’

  ‘Really, Mr Hume. For an intelligent man you can be remarkably stupid at times. Tell me first, though, where is your young friend, Mr Adam Smith?’

  ‘He is well beyond you, L’Arquen,’ Hume spat back. ‘I sent him away this morning. He will be miles from here by now.’

  ‘No. No, I fear you are wrong there, sir. You see, we picked him up on the road many hours ago. He is with us at Craigleven. In fact, he is with Trooper Williams even as we speak. He is my prisoner, you see, rather as you are here if I should but care to choose it.’ He paused as if to think. ‘He is very young, isn’t he? And I’ve no doubt he displays much promise. Do you think he will be sitting there silently while my man speaks to him? And not implicating you in with this nest of traitors and Jacobites we’ve found here? Or, indeed, will you be silent yourself and continue to maintain your own innocence? And refuse to implicate him? Can you really trust him to say the same thing as you? After all, Mr Hume, what were you both doing at the castle in the first place – it looks bad doesn’t it? But I would hate to see either of you hanged for treason. And so I only hope that your young friend will be signing his evidence soon …’

  L’Arquen paused for effect.

  ‘…and not trying to escape.’

  There was another pause while David Hume stared back. But he was quiet now and L’Arquen languidly smiled again.

  ‘Very good, Mr Hume. Let us complete our business then. You are to sign this statement without delay. A trap will be coming for you in an hour together with an escort of my men to take you to Wick. You will be reunited with Mr Smith there and you will both take the dawn stagecoach for Edinburgh. Here is your letter of safe passage to show at the checkpoints on the way. And here are five guineas for your expenses on the journey.’

  Hume continued to wait, knowing that there would be more.

  ‘You must be aware of how much I esteem you, Mr Hume. That Treatise of yours was of the first rank. For that reason I don’t believe that you should be misunderstood or mistreated when it becomes known that you gave evidence against Lord Dunbeath. Now, permit me to suggest a proposal that may solve matters. I have a cousin, General James St Clair, and he has been ordered by the Secretary of State to lead a military expedition against the French in Quebec. He is in need of a secretary and I believe you could be just the man for the role. I have taken the liberty of preparing a letter of introduction for you to give to him in London and I’m quite sure it will suffice when you meet him there. I would not return to Scotland for some time if I was you.’

  L’Arquen walked over to the table in the alcove and picked up a quill and an inkwell. He brought them back to the fireplace.

  ‘Now, Mr Hume. You have not yet signed. Come along there, please don’t try my patience. The earl is dead. You should be looking after yourself now.’

  David Hume sighed and looked past where L’Arquen was standing and out through the great curved window to the sea beyond. He was quite calm now. There was nothing else the man could do to threaten him.

  ‘Do you know the truth of why I came here, Colonel L’Arquen?’ he said quietly. ‘Lord Dunbeath had invited me to Caithness to play a game he’d created – he thought to convince me about how the powerful succeed but instead it showed how virtue wins in life. I didn’t come here for politics or rebellion and nor did Adam Smith. You know that. We came here to experiment with Dunbeath’s game. He called it the Prisoner’s Dilemma and it explained how co-operation has evolved in us humans to be the cornerstone of a healthy society. We played it often and discovered how the tramplers in life, people like yourself, will always ultimately lose. We called you hawks, you know. You would probably tell me that you would be pleased to be called that.’

  ‘How very revealing,’ replied L’Arquen smoothly, in a tone of blank disinterest, ‘I must confess that I do not feel as if I have been a loser. Quite the reverse, I rather feel as if I have won.’ He picked up the quill and handed it to Hume. ‘No doubt you’ll be telling me next that this co-operation of yours disagrees with the conclusions of Thomas Hobbes. And that his idea of a social contract is wrong. You know, Mr Hume, you and Smith are exactly the kind of frail creatures – dreamers and ninnies – who most need my kind of authority to guarantee your freedom. You are among the most feeble in life. Without strong leaders like myself to organise and protect you, you people wouldn’t last a month on your own. You’re all as useless as children.’

  ‘No, colonel,’ said Hume, and his voice had quite recovered its strength. ‘Your type will always lose in the end. You may win now but be pleased with your victory while it lasts. You will always be seen for what you are, a defector, a selfish snatcher, unlovely and unloved, a man to be avoided.’

  Hume leant forward and signed his name with a flourish.

  ‘There. That’s over. Please go now, Colonel L’Arquen. We have nothing left to say to each other.’

  L’Arquen smiled again as he leant down to put Hume’s statement in his case.

  ‘Actually, I do have one last question for you, Mr Hume.’

  Hume groaned silently and his heavy shoulders sagged.

  ‘Yes, what is it?’

  ‘I dare say the army will be in Edinburgh before too long. When we’ve crushed this pathetic uprising of yours. I’ve no doubt we shall have to spend time there putting in some proper leadership for Scotland …and I’d be obliged if you’d give me the name of your tailor. I have much admired his work and I notice that you do too, always stroking that embroidered stuff at your wrist.’

  Hume stared at the colonel. There was a long silence. No words came to him.

  ‘No?’ said L’Arquen eventually, a smirk flickering across his face. ‘No matter, Mr Hume. I imagine I shall be able to struggle on with that fellow of mine in Jermyn Street.’

  He picked up his hat from where he’d left it by the fireplace and laughed for a final time.

  ‘Enjoy Quebec, Mr Hume,’ he said. ‘Enjoy Quebec.’

  Acknowledgements

  At the heart of this book are the bones of a short story by Sir Arthur Conan Doyle called ‘The Man from Archangel’. I always thought it was a wonderful tale and, in my enormous gratitude to the Master for using its outline, I have retained the names of the pair in his narrative, Alexis and Sophie.

  The pieces on navigation were influenced by Dava Sobel’s book, Longitude, the story of John Harrison’s long fight to have his marine chronometers recognised as the inventive masterpieces they were and to win the Longitude Prize. The story is one of terrible injustice and deceit as the celestial navigation establishment conspired to make it impossible for him to win.

  Perhaps perversely, I have chosen to make Dunbeath represent that entrenched scientific position.

  Interestingly, as in the story here, it was indeed the intervention of a king, the very English George III though rather than his father, the more Germanic George II, who insisted that Harrison’s genius should be rewarded.

  The central idea in this book, of course, is the conceit that the characters in the story have invented game theory, two hundred years before it was actually formalised. As I understand it, many of the theory’s conclusions that are in the book were indeed expounded by David Hume in his Treatise and elsewhere, but they were arrived at without the kind of mathematical basis that’s imagined here. And, as for Adam Smith’s views, it was true that he was at his most uncertain when he tried to offset his insights into how markets work with what he called a need in humans for ‘sympathy’ towards one another. However, any story that relies as heavily on game theory as this one does cannot fail to acknowledge its debt to John von Neumann, the brilliant p
olymath whose original ideas were first published in 1944 in The Theory of Games and Economic Behaviour.

  It was two colleagues of von Neumann’s at the RAND Corporation some years later who came up with the idea for the Prisoner’s Dilemma while working on irrationality analysis. It’s formed the centerpiece for game theory ever since and large scale, computer-driven competitions were, and still are, run to find the optimal point scoring solutions. It was as a result of these events that one of the leading participants in the field, Anatol Rapoport, originated Tit for Tat and Generous.

  While many of game theory’s major concepts such as zero sum games, hawks and doves, free riders, tragedy of the commons, the dollar auction and so on are quite well known, I have tried to reduce the concepts behind them into a chain of logic to fit with, and hopefully illustrate, the story. Any errors are entirely mine in those places where I felt the unfolding of the tale was more important than getting the theory or the philosophy wholly accurate. I hope so anyway.

  I’m indebted to a number of books that I raided for guidance. In particular, The Evolution of Co-operation by Robert Axelrod, The Logic of Life by Tim Harford, The Selfish Gene by Richard Dawkins, A Beautiful Mind by Sylvia Nasar (a biography and later Oscar winning movie about John Nash, an economist who won the Nobel Prize for his work on game theory and whose Nash Equilibrium Dunbeath says is ‘like many a marriage’) and The Prisoner’s Dilemma by William Poundstone. This last is not only a biography of John von Neumann but also a social history of game theory and more specifically the role that the RAND Corporation put it to during the Cold War and the nuclear arms race.

  But, more than any other, I must acknowledge my debt to Matt Ridley whose brilliant book The Origins of Virtue had me staring out of the window when I first read it fifteen or so years ago and which forms the basis of many of the arguments in this story.

  Wilson Mizner once said that if you borrow from one author it’s plagiarism but if you borrow from lots it’s research …so, if in the course of my research I have lifted a thought or phrase from any of these books in too amateurish a manner then I can only apologise and hope that imitation is indeed regarded by their authors as the sincerest form of flattery.

  I’m also grateful to a number of other writers and their books including Game Theory at Work by James Miller, The Compleat Strategist by JD Williams, Game Theory: A Nontechnical Introduction by Morton D Davis and Game Theory by Ken Binmore.

  As to the book itself, I’m hugely indebted to the many people who read it at various stages and whose advice and help were so important to me. I’d particularly like to thank Stephen Durbridge, who saw the story in an earlier form and who was tremendously encouraging about it and suggested that I turn it into a novel; and William Boyd, who so generously gave up his time to read an early draft and then offered me enormously helpful counsel and direction on the writing. I’d also like to thank Susanne Burri of the LSE for her suggestions on the philosophy, Luke Meynell for his advice on the army in Scotland and Stuart Carnegie for his help with the Baltic, tides, winds and sailing. Many people read the book and I’m particularly grateful for the views and advice I received from Patsy Pollock, Christopher and Carola Chataway, Don Boyd, Charles Sturridge, Paul and Marie Kingsley, Geoff and Dawn Culmer, Ros Levin, Don Grant, my daughter Lucy Davenport and her husband Dominic, my niece and nephew, Charlotte and Simon D’Arcy and my sons, Kerin and William. My agent, Piers Russell-Cobb and Tariq Goddard of Zero Books each gave me huge encouragement and help and I’m enormously grateful to them both. Last, of course, I’d like to thank Gillie, my wife, for her insights when she read the manuscript and for all her love and support during the long writing of this book.