The Prisoner's Dilemma

by Sean Stuart O'Connor

  ‘Indeed, you might say that it would be a foolish man who sat idly by while his neighbour took so much of the available pasture that it was to his own detriment. The logical outcome of this is that he would be bound to respond. He, too, would put out more cattle, the rest of the commoners would also respond until – of course, you can see where I am going with this argument – the land collapses. It becomes overgrazed and can’t recover. And then everyone in society suffers. Selfishness has led to the downfall of the whole community. Indeed, I have heard this phenomenon described as the ‘Tragedy of the Commons’.

  ‘I’m sure you can see the reasoning: when individuals act independently of each other and rationally consult their own self-interest then they will ultimately deplete a limited resource, even when it is clearly not in their interest to do so. In fact, one can imagine that after a certain point where the depletion is advanced, people will behave in an increasingly selfish manner to snatch at whatever is left. They’d be fools not to.’

  ‘How intriguing,’ said Hume when Smith finally brought his gaze back from the sea and had begun once more to see where his feet were landing. ‘I must say that in that case it’s hard to escape the conclusion that where an end is in sight – a finite resource is a good example – then people’s behaviour would be viewed by society as a series of one-time Prisoner’s Dilemmas. Just like Lord Dunbeath’s original game. And, like that, defection would be the only conceivable option. The benefits of co-operation would have broken down. The strategy no longer works.’

  There was a silence while Smith was evidently thinking this through.

  ‘In fact, I think the same mechanism works everywhere. Even the educated classes fall victim – the very people who would look to govern the peasants and commoners. Didn’t we see exactly the same deranged behaviour twenty years or so ago with what was called The South Sea Bubble? Wasn’t that caused because there were a limited number of shares available and a kind of madness overcame people to acquire them – whatever the price?’

  He paused and stared at his feet again.

  ‘I would say there could be another way of looking at this,’ he said at last. ‘I remember you telling me of the early games with Dunbeath and of how you were close to returning to Edinburgh. Perhaps there is an equivalent in society? Where a whole section of co-operators – or at least people who would think of themselves as co-operators – simply leaves the others to what they regard as their errors, and remove themselves.’

  ‘Do you have an example of what you mean?’ replied Hume.

  ‘Well, do you recall the Pilgrim Fathers?’ continued Adam Smith. ‘Instead of continuing their conflict with a society they disagreed with, they left and set up afresh in the American colony. How appropriate that they should have called it the New World!’

  ‘How good it is to have you here, Smith,’ Hume smiled when he heard this. ‘You have set your finger on a sore I have been avoiding. And it is this …how does society control itself while the Dilemma’s internal forces are working themselves through? If you recall, the immortal Thomas Hobbes faced up to this in that great work of his, Leviathan. His view was that man’s selfish nature needed laws to stop him from descending into evil. That he needed the guiding hand of kings or religion or legal restraint to stop him from destroying himself. Do you remember the famous words he used to describe what would happen if this didn’t happen? “No arts. Continual fear and danger of violent death. And the life of man, solitary, poor, nasty, brutish and short.”’

  Hume shook his head, smiling to himself at the power of the words.

  ‘But can we say that he was wrong?’ he continued. ‘Is the Dilemma telling us that all man needs to do is to trust? That the Dilemma’s natural forces will prevail? Can we really believe that when defectors occur they will ultimately fail because, just as the hawks thrived for a time but then declined because they had to end up meeting each other, their very nature leads to their mutual destruction?’

  Smith nodded in agreement.

  ‘Yes, I think something like this must be happening,’ he said. ‘You told me how Miss Kant’s theory was that the early Christians undermined the very Hobbesian nature of the Roman empire. But it took centuries. In just the same way I imagine that the underlying success of co-operation will always win. However, it takes a very long time. In the meantime, there is much repression, unfairness, tyranny and death. Oppressive regimes may fail but they do so only at a huge price to the people in that society. And also in giving people the accepted wisdom that man is essentially bad.

  ‘I must say that your work on the Dilemma has made me completely revise my outlook on the nature of society in general. I had thought at first that individuals had enough common interest in the future to make them combine to create a society that excluded people they thought were destructive.’

  Adam Smith had come to a stop on the path and he now turned to Hume.

  ‘But when I heard from you about the findings from the Prisoner’s Dilemma,’ he continued, ‘I thought that what was really going on was not that people were protecting society in this way but that society itself was the result of individuals striving in their own self-interests. Society, if you like, was a by-product of an efficient market.

  ‘However, I must confess that since I have arrived here I have thought again. I now see that the underlying principle of the Dilemma is the search for the right partners, people that one can trust. Once people have found these new partners they are then able to precipitate out of a society of hawks leaving these so-called selfish rationalists to their fate. They avoid them. In other words, rather than have retaliator doves, the doves simply leave the hawks to their own fate and go off to form a new society.

  ‘Perhaps the virtuous are virtuous for no other reason than that it enables them to join forces with others who are virtuous – to their mutual benefit. Because they have defined themselves in that way and are convinced that it suits them to get together. They have stopped being individuals and have become a group!’

  Hume stroked the embroidery on his coat sleeve and laughed as a great wave of satisfaction swept through him.

  ‘Mr Smith! I’ve rarely heard anything so elegant!’

  They walked on until they reached the headland, each of them deep in their own thoughts. As they looked out to sea Hume turned once again to Adam Smith.

  ‘Well, you’ve certainly given me a way through the tangle I was in such difficulties with. Then light my way, please, through one last problem. Let us take one of these societies you describe as having broken away. Precipitated out as you called it. A society of doves. Very well, according to you, everyone in it is trusting each other and indulging in constant three point relationships. My question is this – does such a society not stultify? Good lord, doesn’t this utopia of theirs suffer from a lack of challenge? How would anything ever change if there were no unreasonable or ambitious men to make it do so? Wouldn’t it decline in ambition if everyone was co-operative? Just as actions have reactions I rather think that it must be inevitable that this general goodness should come under pressure from time to time. After all, do people ever behave better or become more inventive than when they are in danger? Or are having their lives threatened?’

  ‘Hmm,’ murmured Smith, the challenge Hume had put making him stare madly about himself. ‘I would like to ponder on that. There must be much in what you say.’

  * * *

  Zweig was at the helm with Makepeace when Dunbeath came up from sleeping below. The boat was creaming through the waves and Dunbeath looked forward with the wind in his face.

  He turned to look at Zweig, who smiled back at him.

  Dunbeath looked towards the horizon again, his eyes squinting and his face gleaming. He felt completely secure with Zweig. He was quite sure of where he was going. He felt strange. He felt happy.

  Chapter 27

  It was early evening and L’Arquen walked briskly through Craigleven’s stable block, his speed disguising the slight lurch in his
step. As he passed by them, shirt-sleeved troopers stiffened to attention and stopped grooming their horses, only too aware of their colonel’s black mood.

  At the far end of the building, Major Sharrocks stood speaking to one of his men. As he strode up to question him, L’Arquen’s voice could be easily heard by the whole troop.

  ‘Any progress, major?’

  ‘No sir,’ replied Sharrocks smartly, ‘still no sign of them. But I’m sure we shall sight their boat soon. We have two guards at the castle’s entrance and a further man on the dunes.’

  L’Arquen looked at him sourly, as if he’d just received a confession of personal failure.

  ‘Harken, Sharrocks,’ he said in a low voice that nonetheless carried to the others. To a man they froze. ‘Keep looking, keep looking. Report to me immediately you see something.’

  * * *

  The King’s Messenger rode on. He had cut his sleep down to four hours a night but he still felt the journey was never going to end.

  He was now in central Scotland and ahead of him was yet another roadblock, the guards at it calling on him to halt. He pointed to his silver greyhound insignia and shouted down at them.

  ‘King’s Messenger with urgent orders for the 17th Dragoons in Caithness. From Prince von Brunswick-Luneburg! Let me pass. How far to Perth?’

  The man swung the barrier upwards and called back.

  ‘Twelve miles!’

  The messenger galloped on.

  * * *

  Sophie, Hume and Adam Smith were finishing a simple dinner of lamb stew, the dining room lit by lanterns and candlelight. An echo of another dinner in Edinburgh, Hume thought to himself. He listened to Smith as he spoke to Sophie in the chair opposite him, all the time gazing at the far end of the table.

  ‘Hume and I were discussing something on our walk this afternoon, Miss Kant. We spoke about whether society is not the better for being threatened by the occasional defector. His view was that a society of co-operators, constant three pointers, however trusting and supportive it might be, would become complacent and dulled over time. He wondered whether there wasn’t a natural desire in our natures, of which we are quite unaware, that needs the threat of defectors to keep society’s edge sharp and the dream of liberty and fairness alive.’

  ‘Yes, Mr Hume and I have touched on much the same topic, ourselves,’ replied Sophie. ‘Do you have any thoughts on the matter?’

  ‘I have, indeed, been thinking on it. If you’ll permit me to propose them, I believe I do have some views.’

  Adam Smith sat back in his chair and now stared at one of the ceiling bosses.

  ‘I would suggest that there are two great potential threats that must be constant reminders of the need for vigilance, however settled or co-operative a society may appear.

  ‘The first is the madman. The person for whom neither losing nor winning are important. This kind of man is deadly to others because he rejects the concept of a repeated Prisoner’s Dilemma. For his own reasons, perhaps a warped background, perhaps bitter experiences – or possibly he simply has too much power or security and thinks he has no need to care about the reactions of other people – whatever his motive is, he views every choice and exchange as a one-time game. These people are the tramplers in life. For whatever reason, they are completely unafraid of, or unable to see, what you have called the ‘shadow of the future.”

  Sophie nodded.

  ‘I quite agree,’ she replied with a light laugh. ‘They are impossible to deal with. We may have had some experience of that here in these past few weeks. And what do you see as the other threat?’

  ‘Let me ask you something before I answer that,’ said Adam Smith. ‘Let us imagine that you and I are playing the Dilemma. We have agreed to play a game of a hundred turns. This is unusual because we’ve decided on a game with a finite limit. It has a clear end in other words. Early in the game, of course, we find that we can trust each other. But has the Dilemma also not shown us that instead of being truly good we are being good for a reason? That we are trying to lure the other person into being co-operative back? And perhaps lure is a good word because what we are really doing is appearing to be co-operative while, actually, we are waiting for the opportunity to make a quick killing at the other’s expense?’

  ‘Really, Mr Smith!’ said Sophie, ‘you are beginning to sound like Lord Dunbeath.’

  ‘Am I? Well think on this. We are on the hundredth turn. This is your last opportunity to make a choice. What will you play now? Let me answer for you because it is difficult to ever imagine you being devious or disloyal. But you would be, Miss Kant. You would be no different to anyone else. You would have to defect. You’d take five points because I would then have no opportunity left to respond, to punish you. You’d be foolish not to. The game would be over.

  ‘But I’d know that you would do this! And so I’d defect on the ninety ninth turn in anticipation of it. Ha! Then again, you’d be bound to know that I would do this so you would inevitably defect before this – on the ninety eighth turn. And so we go back. When would we ever co-operate under this logic? I think of it as a backward induction paradox and it is, I think, where the parlour games we have been playing depart from people’s behaviour in real life. There are ends in life. People choose to bring things to a close and they frequently defect when they do so. How often have we seen this in friendships? The closer that people have been, the greater the bitterness is when one lets the other down. Am I not right?’

  ‘It’s difficult to argue with your logic,’ broke in Hume as Sophie dropped her head, deep in thought about what Smith had just said. ‘But when do we ever play in life in the knowledge that we have a finite number of turns?’

  ‘Quite,’ replied Smith with all the steeliness of a hunter closing in on his prey. ‘That is the exact point I was about to make. Let us return to who is the most dangerous player. Is he not the person who knows that only he is playing a finite game when everyone else thinks that they are repeating forever? He is the ultimate betrayer. Unknown to the other players, indeed to society as a whole, he is planning on grabbing five points because only he knows that the game is coming to an end. While all the good, trusting, three-point wishing people think it is continuing, he has lured them into looking away, but only so he can stab them in the back.’

  Sophie seemed to come out of a daydream as Adam Smith reached the end of his argument.

  ‘Yes, I see your point,’ she now said slowly. ‘He is a super free rider, isn’t he? He doesn’t defect knowing that he’s going to continue to live in that society. He knows he won’t be. He doesn’t mind dealing it a mortal blow because he knows he won’t have to deal with the people ever again. Yes, he is indeed dangerous. Perhaps this is why we hate betrayal so much? And perhaps this accounts for why society reserves its greatest contempt and most severe punishments for traitors?’

  * * *

  Evening was falling as Zweig looked closely at the coast. He studied the shape of the cliffs as they snaked into the distance and then referred back to some rudimentary charts that he’d found in a forward locker on the boat.

  ‘I believe that is Calghoustie Head,’ he said to Dunbeath, pointing to a spit of land. ‘With this wind on our beam there is every chance we shall see the castle tonight.’

  They sailed on, with Zweig piling on yet more canvas as the thought of journey’s end made the men urge the little craft forward. The wind freshened and moonlight lit their path. At about two the following morning they rounded a headland and the enormous fortress came into view in the distance.

  ‘There it is, my lord, The Castle of Beath,’ said Zweig. ‘You must be pleased to be back.’

  ‘Yes, I am indeed’ replied Dunbeath, and he squinted into the breeze to look at it. He stood studying its outline for some seconds but stiffened as something caught his eye and he became quite still, concentrating his gaze forward.

  ‘What’s that hanging down from the observatory?’ he murmured. ‘Pass me that glass, Zweig, i
f you’d be so kind.’

  He took the telescope that Zweig handed him and focused it. The enlarged image swam into view. It showed a huge white cloth, suspended from the battlements of the Grey Tower.

  ‘It looks like they’ve hung a bed sheet up there, captain,’ said Dunbeath, his eye still to the glass. ‘It must be a white flag – does that mean they’ve surrendered in some way? Here, look for yourself.’

  Zweig took the telescope and with the practiced art of a mariner he focused on the castle for a moment. He adjusted the setting and then set it down.

  ‘No, my lord, I don’t believe it is a white flag. I think it’s what you first said it was. It is indeed a bed sheet. You speak excellent German, as you know, but perhaps your knowledge of the language has been shaped mainly by your scientific interests. It could be that you do not know some of our more domestic terms. The German word for bed sheet is spelt Laken but we pronounce it…’

  ‘L’Arquen!’ said Dunbeath, grimly.

  ‘Yes, my lord, Sophie would assume that we’d understand the sheet’s meaning. I’m afraid she’s warning us that the colonel is aware of our trip and I’ve therefore no doubt that the English are at the castle. If L’Arquen knows where you’ve been then he’ll know that I’m with you too. And, therefore, we have to assume that he’ll know who I am – and that, I fear, would put you in great danger for consorting with me. He’d be bound to conclude that I was bringing the powder and munitions for you.’