Saturday morning as I took my son to his friend’s birthday party, I was greeted by a queue of traffic about a mile long (luckily in the opposite direction). They were queuing for our local petrol station. Still today there is chaos in the UK as most petrol stations experience long queues or run out altogether. Now also in a panic, UK government has even suspended the application of competition law in petrol retail – so fuel suppliers can coordinate on managing the shortage.

Is this an example of mass psychogenic illness as commentators and government ministers seem to suggest? After all, there really is no underlying shortage whatsoever. No, this isn’t madness, it’s pure game theory.

In my studies it was drilled in to me by the great game theorist Peyton Young that a Nash equilibrium isn’t just a set of strategies. It’s also a set of beliefs.

You probably already know what a Nash equilibrium is – the foundational concept of game theory. A solution in which every player’s strategy is the best available, given what every other player is doing. What is the role of beliefs in all this? Well the simple fact is that most of the time I have no idea what your strategy actually is. I have to guess, based on what’s rational for you to do. I need some beliefs about your strategy.

And, to make things worse, your optimal strategy depends on what you believe about me. So I need beliefs about your beliefs. And, like fleas to bite ‘em, those beliefs need more beliefs, so on ad infinitum.  

Why does this matter?

It matters when it comes to panic buying. I believe there is no real shortage. You believe there is no real shortage. And I believe you believe that. But that’s not enough. I have to believe that you believe I believe that. And you need to believe that I believe that. And so on. If I think you believe other people believe in the shortage, I might worry about your behaviour just the same. In game theory it’s called the problem of “almost common knowledge” – where theory shows that with even just a little bit of doubt in the system, behaviours can start to depart radically from the outcome when we have confident beliefs about beliefs.

Let’s say I think there are just a small number of people who actually believe there is a shortage of fuel. They will all be off to the pumps for sure. Then, after them, there are some people who don’t really think there IS a shortage, but who think there COULD be a shortage if more people than normal fill up this weekend. And I believe they might act like there could be a shortage. And expectations of their behaviour might even be enough to tempt some others out there to join the queue. Then I know that any queues will be in the press, and that for sure will be enough to get a bunch of people worried. And so on ad infinitum.

It’s entirely possible that I can rush to the pumps despite the fact that (1) I believe without any doubt that there is no real shortage, and (2) I believe almost all people agree with me. The fact that I’m certain you see no real shortage is irrelevant. Because I know your actual behaviour will be a function of what you believe about other people. 

If the circumstances are right, it might be enough to think that there are only a small number of people genuinely concerned about a shortage. Beliefs take care of the rest. It becomes the definition of a self-fulfilling prophecy.

That is why it is categorically stupid for ministers to go out publicly saying “there is absolutely no fuel shortage!” as they did on Friday night. Sending that message tells the public unequivocally that there must be SOME people who already believe there is a shortage. And bingo, that’s enough to make a rush to the pumps entirely rational. 

TL;DR – glad I bought an electric car.