I don’t understand the logic of this. Does seem like game-theoretically the net-payout is really what matters. What would be the argument for something else mattering?
BEORNWULF: A messenger from the besiegers!
WIGMUND: Send him away. We have nothing to discuss with the norsemen while we are at war.
AELFRED: We might as well hear them out. This siege is deadly dull. Norseman, deliver your message, and then leave so that we may discuss our reply.
MESSENGER: Sigurd bids me say that if you give us two thirds of the gold in your treasury, our army will depart. He reminds you that if this siege goes on, you will lose the harvest, and this will cost you more dearly than the gold he demands.
The messenger exits.
AELFRED: Ah. Well, I can’t blame him for trying. But no, certainly not.
BEORNWULF: Hold on, I know what you’re thinking, but this actually makes sense. When Sigurd’s army first showed up, I was the first to argue against paying him off. After all, if we’d paid right at the start, then he would’ve made a profit on the attack, and it would only encourage more. But the siege has been long and hard for us both. If we accept this deal *now*, he’ll take a net loss. We’ve spent most of the treasury resisting the siege—
WIGMUND: As we should! Millions for defense, but not one cent for tribute!
BEORNWULF: Certainly. But the gold we have left won’t even cover what they’ve already spent on their attack. Their net payout will still be negative, so game-theoretically, it doesn’t make sense to think of it as “tribute”. As long as we’re extremely sure they’re in the red, we should minimize our own costs, and missing the harvest would be a *huge* cost. People will starve. The deal is a good one.
WIGMUND: Never! if once you have paid him the danegeld, you never get rid of the Dane!
BEORNWULF: Not quite. The mechanism matters. The Dane has an incentive to return *only if the danegeld exceeds his costs*.
WIGMUND: Look, you can mess with the categories however you like, and find some clever math that justifies doing whatever you’ve already decided you want to do. None of that constrains your behavior and so none of that matters. What matters is, take away all the fancy definitions and you’re still just paying danegeld.
BEORNWULF: How can I put this in language you’ll understand—it doesn’t matter whether the definitions support what *I* want to do, it matters whether the definitions reflect the *norsemen’s* decision algorithm. *They* care about the net payout, not the gross payout.
AELFRED: Hold on. Are you modeling the norsemen as profit-maximizers?
BEORNWULF: More or less? I mean, no one is perfectly rational, but yeah, everyone *approximates* a rational profit-maximizer.
WIGMUND: They are savage, irrational heathens! They never even study game theory!
BEORNWULF: Come on. I’ll grant that they don’t use the same jargon we do, but they attack because they expect to make a profit off it. If they don’t expect to profit, they’ll stop. Surely they do *that* much even without explicit game theoretic proofs.
AELFRED: That affects their decision, yes, but it’s far from the whole story. The norsemen care about more than just gold and monetary profit. They care about pride. Dominance. Social rank and standing. Their average warrior is a young man in his teens or early twenties. When he decides whether to join the chief’s attack, he’s not sitting down with spreadsheets and a green visor to compute the expected value, he’s remembering that time cousin Guthrum showed off the silver chalice he looted from Lindisfarne. Remember, Sigurd brought the army here in the first place to avenge his brother’s death—
BEORNWULF: That’s a transparent pretext! He can’t possibly blame us for that, we killed Agnarr in self-defense during the raid on the abbey.
WIGMUND: You can tell that to Sigurd. If it had been my brother, I’d avenge him too.
AELFRED: Among their people, when a man is murdered, it’s not a *tragedy* to his family, it’s an *insult*. It can only be wiped away with either a weregeld payment from the murderer or a blood feud. Yes, Sigurd cares about gold, but he also cares tremendously about *personally knowing he defeated us*, in order to remove the shame we dealt him by killing Agnarr. Modeling his decisions as profit-maximizing will miss a bunch of his actual decision criteria and constraints, and therefore fail to predict the norsemen’s future actions.
WIGMUND: You’re overcomplicating this. If we pay, the norsemen will learn that we pay, and more will come. If we do not pay, they will learn that we do not pay, and fewer will come.
BEORNWULF: They don’t care if we *pay*, they care if it’s *profitable*. This is basic accounting.
AELFRED: They *do* care if we pay. Most of them won’t know or care what the net-payout is. If we pay tribute, this will raise Sigurd’s prestige in their eyes no matter how much he spent on the expedition, and he needs his warriors’ support more than he needs our gold. Taking a net loss won’t change his view on whether he’s avenged the insult to his family, and we do *not* want the Norsemen to think they can get away with coming here to avenge “insults” like killing their raiders in self-defense. On the other hand, if Sigurd goes home doubly shamed by failing to make us submit, they’ll think twice about trying that next time.
BEORNWULF: I don’t care about insults. I don’t care what Sigurd’s warriors think of him. I don’t care who can spin a story of glorious victory or who ends up feeling like they took a shameful defeat. I care about how many of our people will die on norse spears, and how many of our people will die of famine if we don’t get the harvest in. All that other stuff is trivial bullshit in comparison.
AELFRED: That all makes sense. You still ought to track those things instrumentally. The norsemen care about all that, and it affects their behavior. If you want a model of how to deter them, you have to model the trivial bullshit that they care about. If you abstract away what they *actually do* care about with a model of what you think they *ought* to care about, then your model *won’t work*, and you might find yourself surprised when they attack again because they correctly predict that you’ll cave on “trivial bullshit”. Henry IV could swallow his pride and say “Paris is well worth a mass”, but that was because he was *correctly modeling* the Parisians’ pride.
WIGMUND: Wait. That is *wildly* anachronistic. Henry converted to Catholicism in 1593. This dialogue is taking place in, what, probably the 9th century?
AELFRED: Hey, I didn’t make a fuss when you quoted Kipling.
BEORNWULF: A messenger from the besiegers!
WIGMUND: Send him away. We have nothing to discuss with the norsemen while we are at war.
AELFRED: We might as well hear them out. This siege is deadly dull. Norseman, deliver your message, and then leave so that we may discuss our reply.
MESSENGER: Sigurd bids me say that if you give us two thirds of the gold in your treasury, our army will depart. He reminds you that if this siege goes on, you will lose the harvest, and this will cost you more dearly than the gold he demands.
The messenger exits.
AELFRED: Ah. Well, I can’t blame him for trying. But no, certainly not.
BEORNWULF: Hold on, I know what you’re thinking, but this actually makes sense. When Sigurd’s army first showed up, I was the first to argue against paying him off. After all, if we’d paid right at the start, then he would’ve made a profit on the attack, and it would only encourage more. But the siege has been long and hard for us both. If we accept this deal *now*, he’ll take a net loss. We’ve spent most of the treasury resisting the siege—
WIGMUND: As we should! Millions for defense, but not one cent for tribute!
BEORNWULF: Certainly. But the gold we have left won’t even cover what they’ve already spent on their attack. Their net payout will still be negative, so game-theoretically, it doesn’t make sense to think of it as “tribute”. As long as we’re extremely sure they’re in the red, we should minimize our own costs, and missing the harvest would be a *huge* cost. People will starve. The deal is a good one.
WIGMUND: Never! if once you have paid him the danegeld, you never get rid of the Dane!
BEORNWULF: Not quite. The mechanism matters. The Dane has an incentive to return *only if the danegeld exceeds his costs*.
WIGMUND: Look, you can mess with the categories however you like, and find some clever math that justifies doing whatever you’ve already decided you want to do. None of that constrains your behavior and so none of that matters. What matters is, take away all the fancy definitions and you’re still just paying danegeld.
BEORNWULF: How can I put this in language you’ll understand—it doesn’t matter whether the definitions support what *I* want to do, it matters whether the definitions reflect the *norsemen’s* decision algorithm. *They* care about the net payout, not the gross payout.
AELFRED: Hold on. Are you modeling the norsemen as profit-maximizers?
BEORNWULF: More or less? I mean, no one is perfectly rational, but yeah, everyone *approximates* a rational profit-maximizer.
WIGMUND: They are savage, irrational heathens! They never even study game theory!
BEORNWULF: Come on. I’ll grant that they don’t use the same jargon we do, but they attack because they expect to make a profit off it. If they don’t expect to profit, they’ll stop. Surely they do *that* much even without explicit game theoretic proofs.
AELFRED: That affects their decision, yes, but it’s far from the whole story. The norsemen care about more than just gold and monetary profit. They care about pride. Dominance. Social rank and standing. Their average warrior is a young man in his teens or early twenties. When he decides whether to join the chief’s attack, he’s not sitting down with spreadsheets and a green visor to compute the expected value, he’s remembering that time cousin Guthrum showed off the silver chalice he looted from Lindisfarne. Remember, Sigurd brought the army here in the first place to avenge his brother’s death—
BEORNWULF: That’s a transparent pretext! He can’t possibly blame us for that, we killed Agnarr in self-defense during the raid on the abbey.
WIGMUND: You can tell that to Sigurd. If it had been my brother, I’d avenge him too.
AELFRED: Among their people, when a man is murdered, it’s not a *tragedy* to his family, it’s an *insult*. It can only be wiped away with either a weregeld payment from the murderer or a blood feud. Yes, Sigurd cares about gold, but he also cares tremendously about *personally knowing he defeated us*, in order to remove the shame we dealt him by killing Agnarr. Modeling his decisions as profit-maximizing will miss a bunch of his actual decision criteria and constraints, and therefore fail to predict the norsemen’s future actions.
WIGMUND: You’re overcomplicating this. If we pay, the norsemen will learn that we pay, and more will come. If we do not pay, they will learn that we do not pay, and fewer will come.
BEORNWULF: They don’t care if we *pay*, they care if it’s *profitable*. This is basic accounting.
AELFRED: They *do* care if we pay. Most of them won’t know or care what the net-payout is. If we pay tribute, this will raise Sigurd’s prestige in their eyes no matter how much he spent on the expedition, and he needs his warriors’ support more than he needs our gold. Taking a net loss won’t change his view on whether he’s avenged the insult to his family, and we do *not* want the Norsemen to think they can get away with coming here to avenge “insults” like killing their raiders in self-defense. On the other hand, if Sigurd goes home doubly shamed by failing to make us submit, they’ll think twice about trying that next time.
BEORNWULF: I don’t care about insults. I don’t care what Sigurd’s warriors think of him. I don’t care who can spin a story of glorious victory or who ends up feeling like they took a shameful defeat. I care about how many of our people will die on norse spears, and how many of our people will die of famine if we don’t get the harvest in. All that other stuff is trivial bullshit in comparison.
AELFRED: That all makes sense. You still ought to track those things instrumentally. The norsemen care about all that, and it affects their behavior. If you want a model of how to deter them, you have to model the trivial bullshit that they care about. If you abstract away what they *actually do* care about with a model of what you think they *ought* to care about, then your model *won’t work*, and you might find yourself surprised when they attack again because they correctly predict that you’ll cave on “trivial bullshit”. Henry IV could swallow his pride and say “Paris is well worth a mass”, but that was because he was *correctly modeling* the Parisians’ pride.
WIGMUND: Wait. That is *wildly* anachronistic. Henry converted to Catholicism in 1593. This dialogue is taking place in, what, probably the 9th century?
AELFRED: Hey, I didn’t make a fuss when you quoted Kipling.
This was fantastic, and you should post it as a top level post.