Multiple Equilibria, Public Policy, and How to Get a Date

Dating in the best of all possible equilibria

It's been a bad month. Your hair's gotten scruffy, you've stopped shaving, and you haven't even thought about cutting your nails. And... somehow, you haven't managed to get any dates. When you wake up in the morning you go to your wardrobe and look at all the beautiful clothes you vaguely remember you used to wear once. "Eh, what does it matter," you think, "no-one is going to date me anyway." You pull on your sweatpants and head out the door.

Your life is in what an economist would call equilibrium: you don't go on dates, so you don't bother with your appearance, so you don't go on dates. Everything is in balance, and (as things stand) the system can continue at exactly the levels of grooming and dating that you're experiencing now.

The TV screen goes wavy for a second and we cut to an alternative universe. Your hair looks fabulous, your skin is smoother than a mango smoothie, and even your mother would have to confess that your nails look great. You can't find enough hours in the day for all the dates you need to go on. When you wake up in the morning you go to your wardrobe and look at the pile of untouched sweatpants lying sadly in a corner, and note to yourself that you really ought to give them away already. You pull on a perfectly matching outfit and breeze out the door.

Once again, your life is in equilibrium: you go on lots of dates, so you take good care of your appearance, so you go on lots of dates. Everything is in balance, and (as things stand) the system can continue at exactly the levels of grooming and dating that you're experiencing now.

But here's the thing: while the two equilibria we see here represent very different outcomes, both are stable in themselves and both can come out of the "same" basic conditions. Economists call this a situation of multiple equilibria.

What determines which equilibrium we end up in, in a particular situation? Who knows. Maybe it's luck, maybe it's historical accident (did you happen to bump into an interesting stranger at a coffeeshop last month, setting off a chain of awesome events?), or maybe a one-off extreme event somehow jolted you into one or other of the possibilities.

Just as importantly: if we're in one equilibrium but we'd like to be in another one, can we make the jump across? Perhaps if there's an external intervention in the system (your friends come over one day, force you into a nicer outfit, and drag you to a party) then we can make the leap from one equilibrium to another. The interesting thing here is that, because an equilibrium is (by definition) a stable situation, once the intervention has happened we will then "naturally" stay at our new equilibrium until and unless another big jolt occurs. On a national policy level, some might argue that this can be a good reason to authorise government intervention in situations where they would otherwise find it too much of an imposition; the argument would be that, in a multiple equilibria situation, the government will only have to intervene in the short term but won't have to sustain that intervention in the long term.

There are many such public-policy examples of (potential) multiple equilibria, but let's look at one: bicylce usage in cities. In one equilibrium, few people in a given city ride bikes so riding a bike is relatively dangerous and inconvenient so few people ride bikes. In another equilibrium, many people in the city ride bikes so riding a bike is relatively safe and convenient and so many people ride bikes. If a city government thinks that the many-bikes equilibrium is better, but finds itself stuck in the few-bikes equilibrium, some would argue that the city government could be justified in creating a large-scale, dramatic intervention (laying bike-lanes, creating a public bike-share, etc) that might "jolt" the city into the equilibrium they prefer. Of course there would still be lots of other factors to consider, but you'll often hear this argument being made implicitly in all kinds of debates about economics and public policy. Things would be much easier if everyone could start these conversations by saying "I think this is a situation of multiple equilibria," so we could debate the issues with that in mind.

Uri Bram writes popular non-fiction books with a conceptual approach to mathematical, scientific and analytical thinking. He is the author of Thinking Statistically and Write Harder.

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