Sometimes I’m glad I learned a bit of game theory
I learned a bit of undergraduate game theory, alarmingly, by teaching the subject to undergraduates. Don’t be so surprised – this happens more often in universities than they’d like to admit. And don’t feel too sorry for my students – I think people who’ve only just learned the topic can be excellent teachers. Since then, I think about game theory a lot. That’s worth remarking on, because I get the impression that game theory is sometimes criticised, either for being too divorced from reality (especially the solution concepts, which no-one knows whether they’re supposed to be predictions or prescriptions), or for just being not that useful.
That criticism is unfair, because actually game theory has been influential in the real world in the past 20 years, mainly through applications of the related field of mechanism design to internet auctions, school admissions, and kidney exchanges (which save lives by matching more people to compatible kidney donors). My doctoral research was around school choice and admissions, and I used a few insights from mechanism design to design a statistical estimation method.
But nowadays, when I think about game theory, I’m usually mulling over big, abstract stuff to do with society. A good example is Kaushik Basu’s book The Republic of Beliefs (which is too dear for me, so I haven’t read it, but luckily I found his working paper (pdf) with the same title). It’s not too much of an exaggeration to say that Basu takes the whole of society, and imagines it as a great big game. Basu asks whether laws could ever be enforced if it were not in the enforcers' (police, courts, armies) interests to enforce them. They enforce them because that’s their job, of course, but what about the people who pay them – would they do it if it weren’t in their interests to do so? And so on. I’m summarising terribly, but you get the idea. You should read the paper.
Thinking about Basu’s thesis this morning, it occurred to me that there’s some sort of a link between that idea, and the concept of a correlated equilibrium in game theory. A correlated equilibrium is a model of how a game might be solved (a “solution concept”) that can sometimes improve upon (in the sense of making everyone better off) the most well-known solution concept, the Nash equilibrium. The difference between a (mixed strategy) Nash equilibrium and a correlated equilibrium is that in the former there is no information exchange between parties – their strategies are independent (uncorrelated). A correlated equilibrium allows strategies to be correlated, and this can be thought of as modelling communication, institutions, systems of rules. The key insight from correlated equilibrium, which echoes that of Basu, is that a system of agreements to act in a particular way is only a solution if it is in each participant’s interests to do so, given what they expect the other participants to do. Traffic lights are a good example. They work because it’s in everyone’s interests to avoid a crash – if only half of people wanted to avoid a crash, and the other half wanted to cause a crash, the institution of traffic lights would break down. For all I know, Basu has a whole chapter on correlated equilibrium in his book. As I said, I haven’t read it.
I haven’t done a good job of articulating why I find Basu’s thesis or correlated equilibrium useful. Part of the problem is that we’re all so used to our institutions just working, more or less. Basu has studied societies where the rule of law doesn’t work so well – states like the DRC, where corruption is rife, enforcers aren’t paid by the state, and society struggles to transition to a better equilibrium.
Game theory has also earned criticism because it has become a cliche – so much so that it has almost become a cliche to ask people to stop referring to everything as a ‘prisoner’s dilemma’. I also think that criticism isn’t fair, because being a cliche is actually a mark of success for a social theory! Since game theory is precise, we can look at each use, and decide whether it fits the model, or whether it’s misused. Another, even more ubiquitous, example is the phrase ‘zero sum’. This is now so well-understood that it has passed into management-speak. But, again, it has done so without losing any of its precision. When your manager talks about some situation not being zero-sum, chances are that the way she’s using the term is no vaguer or less correct than the way a game theorist would use it. And it’s an important concept, because it addresses a common fallacy – the idea that we live in a dog-eat-dog world. So game theory, by passing into cliche, has actually improved common sense!