On the surface, there are big differences between queuing, fashion, and education. But from a game theory perspective, the strategic considerations for each of these areas are surprisingly similar.

In short, these are all arguably examples of failed cooperation due to the individual incentive to escalate.

I will explain what I mean by this in detail below. For now, let’s examine the game of waiting in line to get a framework for analysis.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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Why do we wait in line?

A couple weeks ago I went to see a newly released movie in a theater. To make sure we got good seats in the theater, we showed up an hour early.

But guess what? We weren’t even the first people in line! At least 10 people decided it was better to stand in line even earlier.

While I waiting in the line, I thought about how wasteful it was to wait for the movie. Here we were just standing around on a perfectly good Friday night when we could have been doing something fun instead.

Why does this happen? This is not hard to understand from a game theory perspective.

The game of waiting in line is defined by two strategic considerations. One aspect is that waiting in line is boring, and waiting for a longer time is a waste of time. The other aspect is that people who show up early can pick better seats, so clearly one would want to show up before the crowds.

If everyone simply showed up at the movie near its showtime, then there would be no line and seats would be chosen nearly randomly. So everyone gets the payoff of sitting in an average seat.

But this cannot be an equilibrium. Someone will decide to defect from the group and show up 5 minutes early. I mean why not? Rather than showing up on time and getting an average seat, you could show up early and get the best seat in the house. That’s certainly worth 5 minutes of waiting.

Of course, this logic will appeal to many moviegoers, and so it ends up being the case that lots of people show up 5 minutes early. Suddenly the game has changed: now so many people show up 5 minutes early, that showing up 5 minutes early only gets you an average seat!

And so, repeating the logic one would consider showing up 10 minutes early, then 15 minutes early, and so on. It’s not totally uncommon to have people camp out hours or even a whole day for the opening of a huge blockbuster.

The result is an extremely wasteful equilibrium. People will wait in lines for a movie in a response to the fact that else is waiting in line too.

What we have here is a failure of coordination.

In theory, theaters could eliminate movie theater lines altogether. Theaters could simply assign seats or make it illegal for people to show up early. Or, they could equally as well assign seats at random: as people showed up, their ticket could be scanned and they would be assigned a seat.

But naturally theaters are happy to encourage long lines, which generate buzz and likely increase concession sales for hungry and bored moviegoers waiting in line.

So the game of waiting in line is driven by consumer escalation that profits the theaters. As I’ll explain next, this is the same type of game for why people might wear high heels.

High heels: who is tallest?

Can you see the connection between waiting in line and wearing high heels?

Women could all agree to not wear high heels. Each person would walk proudly in comfortable shoes and stand at her natural height, and not bear the expense of buying a shoe.

But if everyone did this, there is a natural temptation for someone to defect from the group. One woman is going to think it’s advantageous to wear shoes with a little lift to look taller and be more attractive.

When a few women start wearing high heels, it becomes more tempting that other women would want to wear them as well.

Eventually everyone feels it’s sensible to wear high heels. Notice the connection with waiting in line: people are doing something wasteful only because everyone else is doing it too.

Fashion designers could agree not to make high heeled shoes, knowing that they are uncomfortable and make it hard for women to walk. Heck, there is even some evidence that high heeled shoes are genuinely unhealthy and can cause long term damage to toes, tendons, and bones.

But designers, like movie theaters, are fine with the current situation and lack of consumer coordination.

Students could cooperate, but they don’t

I loved the time I was a student at Stanford, particularly in the great weather of Spring Quarter.

The only problem, as they say, was that classes got in the way. On a given afternoon, I was far more likely to be studying under the fluorescent light at the library than basking in the sun at the lovely outdoor swimming pool.

A couple times I did question my choice. Why was I studying the arcane subject of analysis on manifolds instead of going outside? I mean, I’d likely forget the material in a couple of years, so I might as well skip studying and enjoy the weather.

There was definitely a great opportunity for collusion. My math class only had about 8 students. If we all met one day, we could have agreed to study very little for exams. The result would be that we’d all end up getting about the same score (being nearly equally smart). And since the class was graded on a generous curve, we’d all end up with about a B+ for doing very little work!

By now you can deduce why this plan would be hard to execute. There is always some type A personality that would agree to the plan but then secretly study and ruin the curve. Knowing that one person wants to study means it’s also necessary for the rest of us to study as well to avoid getting a bad grade.

Just like in the examples of waiting in line and wearing high heels, there is a circularity to our logic. Again, we are all studying for this final because we know that everyone else is studying too.

This is a game that is a “wasteful” equilibrium for the students, but one with positive results for society. Professors are happy to impart their knowledge (without classes they’d be out of a job!), and society benefits as more individuals get educated.

Summary

Here is a table that shows how the phenomena are similar:

How to win

Each of these games shows an example of failed coordination, resulting in a wasteful outcome for people playing the game.

The horrible part is this: the best strategy in these games is to be more ruthless, more destructive, and more wasteful than other players. For example, it’s the person who camps out the longest who gets the best seat, the woman who wears the fanciest/most expensive high heels who often has the best fashion, and the student that studies day and night who often gets the best grade.

It was a long time ago I figured out how to beat these people. You should not try to beat them at their own game. If you’re not winning the game you are playing, you must change the game and play by your own rules.

A few strategies for these games are:

–wait for a movie to get less popular and lines die down

–forget movie theaters altogether, just wait for home video

–ignore fashion and avoid high heels

–study a specified amount of time, then have fun

–learn for its own sake, not for the grade

None of these strategies is mind-blowing or would appeal to the masses. But I know I’ll win because while others waste time in lines, hurt their bodies, and lose their memorized facts, I’ll look back on evenings I spent doing things, and practicing healthy habits, with an educated mind that can tackle problems analytically.

I am quickly approaching an age in which I have known calculus for more of my life than not. Knowing math has been an invaluable resource as I have tackled money problems and read about the science of our universe origins as a hobby. The knowledge has been far more worth it than the grades. You see, you can win the game if you play by your own rules.

I play for the long run, and I will find a way to win this game.