The Hostage Problem
The Fenris wolf has a problem. He would like to prove his strength by breaking the third fetter as he proved it by braking the previous two that the gods put on him. But he does not trust the gods — would you trust someone who wanted to tie you up? — so will only let them bind him if he has a guarantee that if he cannot break it they will free him.
The gods have a problem. There is no power above them to enforce contracts, so their promise to free him is worthless — and besides, they don’t actually plan to keep it. They try to solve the problem by arguing that if he cannot break it that will prove that he is not strong enough to be a danger to them so they will have no reason to keep him bound, but he isn’t buying that.
The solution Fenrir proposes is for the gods to give a hostage to guarantee performance of their promise. The hostage is Tyr’s right hand. If Fenrir can break the fetter, or if he fails to break it and the gods then free him, there is no problem; he gains nothing by biting the hand off so has no reason to do so. If, on the other hand, they refuse to free him it costs Fenrir nothing to bite down and costs Tyr his right hand. That is a reason for the gods to keep their promise.
As it turns out, it is not a sufficient reason – Fenrir has underestimated just how badly the gods want him bound.
“The Binding of Fenrir” from The Prose Edda by Snorri Sturluson
This is one example of a problem in making contracts self-enforcing, something that it is useful to be able to do if you, like Fenrir and the gods, do not have an authority over you that is willing and able to enforce your contracts.
Consider a less exotic example. I agree to buy a hundred bushels of rice from you for ten dollars a bushel, that being the present market price. I won’t need the rice until next month and have no convenient place to store it so we agree that you will deliver it a month from now. Arranging such contracts takes time, so if at the last minute you decide not to deliver, to default on the contract, I will have a problem. Reselling rice takes time and rice sitting out in the open is likely to spoil, so if when the rice arrives I change my mind and refuse to accept it, you have a problem.
Why might either of those things happen? Someone else might offer you twelve dollars a bushel for your rice, in which case you decide to breach our contract and sell the rice to him. Someone who happens to have rice he no longer needs might offer to sell it to me for eight dollars a bushel, in which case I decide to breach our contract, perhaps at the last minute, and refuse to accept delivery.
One solution to those problems is renegotiation; you tell me that you have another customer willing to pay a higher price and ask if I am willing to match it. But I don’t know if you are telling the truth, may suspect that you are raising the price on me at the last minute because you know it’s too late for me to find an alternative supplier. Similarly in the other direction if, after you deliver the rice, I tell you that I am only willing to pay eight dollars a bushel because I now have an alternative source at that price.
One solution to the risk of my refusing delivery is for you to require a deposit; I pay part of the price in advance, forfeit the deposit if I refuse to accept delivery. But doing that increases your incentive to breach, to keep my deposit and sell the rice a second time to someone else. A solution to the risk of your deciding not to deliver is a reverse deposit; you pay me some money when we sign the contract and get that money back, along with the agreed-on price, when you deliver the rice. But that increases my incentive to refuse delivery and keep your money.
Suppose that instead of giving you a deposit in money I give you a deposit in the form of something valuable to me but of no use to you — my eldest son, who will be your guest until I accept the rice and pay for it. Seizing him, unlike seizing money, does not get you anything, so his presence does not increase your incentive to reneg on the deal. But your refusing to return him does cost me something, so I now have an additional reason to accept delivery of your rice and pay for it.
My son is a hostage. Like Tyr’s hand.
About a century or so before Snorri wrote the Edda, from which I have taken the story of the binding of Fenrir, the same logic played itself out in the real world. The context was the 12th century English civil war between Stephen of Blois, nephew of Henry I, and Henry’s daughter Matilda, both claiming the English crown.
John Marshall was a minor English baron holding Newbury Castle for Matilda. When Stephen attacked the castle, initially without success, John offered him a deal. Give him three days and, if no relieving army showed up from the other side, he would surrender, saving Stephen the cost and risk of another attack. Stephen agreed, on condition that John give William, his second son, as a hostage to guarantee performance of the contract. Stephen, having other things to do with his army, went and did them.
John brought in supplies, hired troops, prepared for a siege. When Stephen returned and demanded surrender, threatening to kill his hostage, John replied that he still had the boy’s brother — also the hammer and anvil with which to forge more sons. Stephen was not sufficiently hard hearted to execute William and the boy was eventually reunited with his family, probably after Stephen and Matilda agreed to a peace treaty making Matilda’s son Henry Stephen’s heir.1
The stories of Tyr’s hand and John Marshall’s son illustrate both the logic of hostages, used to make a contract self-enforcing, and one of the failure modes. King Stephen and the Fenris wolf made the same mistake, overestimating the value of the hostage they held to the other side.
The story of King Stephen and the young William Marshal also illustrates the importance of commitment strategies. Once John had double crossed him there was nothing for Stephen to gain by killing William, whom he had come to like. But if he had been the sort of person who would overcome his scruples and kill the kid, John might have been less willing to double cross him. Making himself that sort of person, someone who would carry out a threat even when doing so no longer served any purpose, might have improved his chances of winning the civil war.
William Marshall grew up to become one of the top tournament knights in western Europe, later one of the most powerful barons in England and ruler, through his wife, of a quarter of Ireland. When King John died there was a French army in London commanded by the heir to the French throne, his claim to the English crown through his wife supported by the barons who were in revolt against John. William accepted the position of regent for John’s nine year old son. Within less than a year the French were defeated, the Barons’ revolt ended, the French army and the Dauphin back in France. If King Stephen had been a little less soft-hearted, England and France might have ended up as a dual monarchy ruled by the King of France.
Two hundred years later the situation reversed. If a sixteen year old peasant girl had not turned out to be a military genius, a divinely inspired saint, or possibly both, England and France might have ended up as a dual monarchy ruled by the King of England.
For a longer discussion of the problem of self-enforcing contracts, past and future, see:
From Imperial China to Cyberspace: Contracting Without the State.
My verses on William Marshal provide additional details: Gesta Gugliemi I, II, III, IV.
A detailed account of the evidence on Joan of Arc by my son William, who argues that her very well document history may be the best evidence we have for the truth of a religion.
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My web page, with the full text of multiple books and articles and much else
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The story is from The History of William Marshal, a biography written shortly after the Marshall’s death. A modern version of the story in verse.
I am interested you say that Joan of Arc was a military genius. I did a very enjoyable podcast with Jonathan Sumption and his view was very much that she was no such thing. Her (decisive) significance was in morale.
These scenarios also remind me of internal corporate politics. While there is nominally a chain of higher powers, they are usually ineffective as arbiters because they don't want to get tied up in it. As a result, a lot of playground tactics end up going around. People break promises and puff themselves up with "what are you going to do about it?".
Maybe we should take more hostages in these situations. "If you want to see your stapler again, you can't keep agreeing to things in private and then badmouthing me in public."