Game theory in Game of Thrones
For those of you who have neither read the novels nor seen the TV series, here is a quick summary: the King of Westeros has died, and his “son” Jeoffrey has been crowned the new King. The old king’s brother alleges (correctly) that Jeoffrey is a bastard, and has claimed the throne for himself. His soldiers sail towards the capital city, King’s Landing, where Tyrion Lannister (Jeoffrey’s dwarf uncle) is preparing the defenses. In a clever move, he sets a large number of enemy ships on fire. However, many soldiers still manage to land, and, despite their best efforts, the first defense falls and Joeffrey’s soldiers have to retreat behind the walls of King’s Landing. King Jeoffrey flees the battle and the soldiers are disheartened. Tyrion rallies them with a speech:
Here’s the first thing you’ll notice about the speech: it’s empty. Tyrion doesn’t really tell them anything that they don’t already know. So why do they respond to it? It’s too easy and cynical to say “because the writers wanted them to” – later in books/show Theon Greyjoy gives an even better speech to his troops, and is knocked out cold and bartered for safe passage. George Martin, the author of the series, is hardly a sucker for nice speeches.
Imagine that you’re a soldier defending King’s Landing. If your side is highly likely to win, you want to stay on the battlefield – you enjoy the thrill of being on the winning side, whatever loot you can pull off the body of dead soldiers, a chance at promotion (contrary to what Tyrion says, key soldiers were in fact given knighthoods), and you won’t be hunted down and executed as a deserter. On the other hand, if you’re highly unlikely to win, you’d rather go home and spend your last hours with your family, perhaps trying to hide or flee, since none of the above thing are likely to happen, and this way you and your family may survive. What you really want to know is this: how likely are we to win?
You don’t really know. Who does? Well… Tyrion Lannister, for one. He has spies in the enemy camps. He knows how many enemy troops sailed to King’s Landing. He blew up enemy ships and has at least a rough idea of how many men died on them. He’s well-read, no doubt in military tactics as well. He’s smart, so if he reaches a conclusion, it’s probably the right one. He’s had a bird’s eye view of the entire battle so far. He’s no doubt studied the city walls, and so if he claims that he knows a way to flank the enemy there is no reason to disbelieve him. If he genuinely believes that we’re likely to win, he’s probably right.
But how do you know he genuinely believes this? Tyrion Lannister would want you to fight, maximizing the probability of a victory, even if the probability is low to start with. He has a strong incentive to lie, so you can’t take his claims at face value. Talk is cheap. What really makes the case is not Tyrion’s speech, but his decision to fight. He has the same incentives as the soldiers – stay if the odds are in their favour and flee otherwise. If he puts his own life on the line, that means the odds probably are in their favour. Of course, he knows this, has more to gain (he’s the scion of a powerful and wealthy house, after all) and less to lose (he has no family, and will probably be ransomed if he is caught) than anyone else, so it’s not enough that he fights – he must lead. He must be at the front of his troops, exposed to the maximum risk.
The above theory is based on a famous paper – Towards an Economic Theory of Leadership: Leading by Example by Benjamin Hermalin. You can find it here. It is painfully mathematical, but the crux of the theory is this: in many cases “leaders” have no authority over people. Rather, they have better information, and must figure out a way of communicating that information in a manner that is convincing, one of which is leading by example. By putting in a lot of effort, you’re signalling that a particular project is worthwhile (because you wouldn’t be putting in this much effort if it weren’t), thus persuading your “followers” to do so as well.