Some simple game theory of discursive conflict
There’s a really widespread belief in the social sciences that discourse matters, that language and narrative isn’t just a transparent medium through which we view the world, but also something that creates winners and losers, and is therefore fought over. Michel Foucault is the obvious name to check here. His idea has been so influential that he must surely have been on to something. Even if you don’t drink the postmodernism Kool-aid, “discourse” is too popular a concept to be completely mistaken.
Economists have not traditionally paid much attention to narratives, but that’s been changing. Some big names have written papers and books, either saying “hey, maybe narrative is important, we should think about it”, or actually trying to think about narrative in the framework of an economic model. This is a bit ironic, because the essence of formal modelling is that you throw out all the thick description and reduce everything to narrative-free mathematics. But OK, fine, economists have to bring their unique approach to bear.
So, let’s look at discourse from a game-theoretic point of view. This is a “paper I’m too lazy to write”, or perhaps one that’s too trivial to write: I’m no theorist, it’s a simple idea, make of it what you will. I’ll focus on discursive conflict — the idea that there might be conflicting interests, and resulting struggles, over how things are described.
Here’s a classic 2 x 2 game: the Battle of the Sexes. Like many such games it has a cute gender-stereotyped story attached.
The story is that Jim wants the couple to go to the boxing, and Jane wants to go to the ballet. Jim chooses an action in the rows; Jane chooses one in the columns. The numbers are his payoff, then hers. So, if they both go to the boxing, Jim gets 2 and Jane gets 1. If they both go to the ballet, Jim gets 1 and Jane gets 2. But they both prefer either of these alternatives to the sad situation where they go to different events alone.
There are two equilibria here: both go to the ballet, or both go to the boxing. Those are equilibria because neither person unilaterally wants to change their action. Still, each equilibrium benefits one person especially. Jim would rather get to the BOX, BOX equilibrium. Jane prefers BALL, BALL.
This story roughly fits many real world situations:
There is a range of prices at which both a buyer and a seller would be better off. But there’s also conflict of interest, because a higher price benefits the seller. Here, the two actions might be BUY HIGH, BUY LOW and SELL HIGH, SELL LOW; if the players can’t agree on a price then there’s no trade.
Society is a “cooperative venture for mutual advantage”: rules and laws are better for everyone than anarchy. But the rich and poor might prefer different kinds of society with different laws. Here the actions might be CAPITALISM, COMMUNISM; if the actors can’t agree then there’s civil war.
As for laws, so for rulers. If everyone agrees that someone is the legitimate power in the land, then it is very risky to try obeying anyone else. So there are as many equilibria as there are potential rulers. Of course, each equilibrium benefits different people — the relevant ruler and his allies.
So, let’s drop the boxing and ballet story, and just write two abstract labels A and B for each action, and two labels 1 and 2 for the players.
Suppose everyone in society is playing the A, A equilibrium, benefiting the player 1s. Of course, in the real world, actions aren’t called A and B, and players aren’t labelled 1 and 2. They’ll be known by some real world labels. Action A might be “respect for private property”. Action B might be “redistribution”. Players 1 and 2 might be “men and women” or “the employer and the employee”.
Is there room for discursive conflict here? Probably not. Everybody knows who the “man” is. Everybody knows that carriages drive on the left, and if you try to redefine left as right, you won’t persuade anyone else, and you might have a nasty accident. You can’t just call yourself the King; if you do, you may end up working in the scullery and think yourself lucky.
But now suppose a new game arises — another Battle of the Sexes. For example:
Say we all know what it means to own land. And we agree that only “the landowner” should be allowed to use his land, graze cows on it, sell it, etc.
Now an inventor claims that he owns his invention. Just like with the land, other people shouldn’t be allowed to use it! Arguments about patents were a big deal in the 17th and 18th centuries, and the development of patent law may have helped propel the industrial revolution. (Or maybe not: those arguments are still going on.)Suppose we know what a newspaper is, and what a private letter is. A newspaper gets sued if a writer in the paper libels someone, but the Post Office doesn’t get sued if someone writes a libellous letter.
Now a new thing arises called the internet. Are content-hosting tech firms like newspapers, or like the Post Office? Who is responsible for the content? There are at least two legal equilibria here, each benefiting different actors.
The stage is now set for different types of discursive conflict.
Type I conflict: relabel the actions
“Pearls before swine,” giggled the white mouse. “Tee, hee!”
“How uneducated you are!” snorted the pig, turning up his snout. “Ladies before gentlemen; swine before pearls!”
— Hugh Lofting, Dr Doolittle’s Post Office
In the old game, everyone is playing action A – whatever they call it. It’s very likely that in the new game, they’ll also play the action with the same label. But which action should have that label? If you can persuade everyone that the action which benefits you is the “real action A”, then you win.
Is an invention private property? Then nobody should steal your property. “Respecting property” means letting inventors patent their ideas. Inventors win. Is an invention just an idea, which anybody is free to talk about? “Respecting property” means allowing firms to produce goods using ideas they’ve heard of. Copycats win.
Type II conflict: relabel the players
The beggars have changed places, but the lash goes on.
— Yeats
You might think that player 1 in the old game has an advantage here. It’s natural to think that if action A benefits player 1 in the old game, then the action which benefits the same person in the new game must also be “action A”, and so then everyone expects everyone else to play it.
But that assumes we directly know the identities of the players. In a small village, maybe everybody knows that Bubba always gets his way, and that expectation works across many different arenas. But in a big society, players are known as members of categories: lords and peasants, men and women, whites and blacks.
Some labels are sticky: it’s hard to change your sex or your ethnic group. People do try, though. And some labels are more context-dependent. We must all obey the king, right? But when the old king dies, who is the new king?
Type III conflict: relabel the game
Now suppose that before the new game arrives, there are already two existing games in society, with settled equilibria. In one, everyone plays A; in the other, everyone plays B. Suppose there are also obvious, settled ways in which the new game’s actions and players map to each of the old games’ actions and players. So there’s no scope for fighting over those labels. But, which existing game is the new game more like? People who prefer A will want it to seem like the first game; those who prefer B will push its similarity to the second. Comparisons and analogies will have real payoffs.
We all know that you need to “protect minorities”. We also all agree that you need to “defend free speech”. And we know who the players are in these stereotyped stories — the insulted minority, the cancelled plain-speaker — and how the story should end — we come together to defend minorities/free speech against angry white men/woke loons. But which story better fits the latest Twitter hullaballoo?
Case-, nut- and basketcase-based reasoning
Under the hood of this argument lies a theory of how people reason about new strategic situations. For the logic to work, players must draw analogies with games they already know about. There are some game-theoretic papers taking this perspective, which indeed seems quite plausible. Work on labelling in coordination games also seems relevant.
Can a game-theory perspective offer any new insights on the phenomenon? Here is one potential hypothesis: in discursive conflict, breadth beats depth. That is, when you’re trying to relabel something so as to change the equilibrium, you don’t have to persuade people about reality. You just need to persuade them about what other people are thinking. Or even about what other people think other people will think. Or… and so on. In the world of the Battle of the Sexes, everybody is just trying to predict what other people will do, so as to go along with it, and they know that everyone else is doing the same thing. If you can make an unconvincing analogy between one player/action/game and another, but you can make it loudly enough, it won’t convince people; but it might convince them that other people will be convinced.
So, it’s more important to spread your message very broadly than to make it deeply persuasive. This might be why the Big Lie remains a powerful technique. Does anyone, apart from a few nutcases, really think the 2020 US election was stolen? That’s not the point, and it’s hard to measure what people “really think”. What matters is that people, especially politicians, know to say they do. If enough of them do that, the equilibrium changes anyway, whatever people’s “real” beliefs. This might be why, as Hannah Arendt put it, “propaganda is marked by its extreme contempt for facts as such”.
That’s all! There’s no deep maths here. I think it is a simple way of bringing game-theoretic reasoning to bear on the study of narrative. There’s an old mathematics joke:
A mathematician is at a conference hotel, working late on his paper. Suddenly he notices that his cigarette ash has set the waste paper bin on fire. Swiftly, he puts the fire out with the fire extinguisher. Then he goes to bed.
The next night he’s working late again, when he spots that his cigarette has set a piece of paper on his desk smouldering. Quick as a flash, he puts the paper into the bin, which is soon cheerfully ablaze. “An already-solved problem”, thinks the mathematician, and he goes to bed.
The mathematician’s logic is that it’s good to reuse your tools. So perhaps it helps to think about discursive conflict using simple games which we already understand.
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