2018-08-20 concepts

The prisoner's dilemma, the ultimatum game, a keynesian beauty contest

Hey all -

Last time, I introduced some high-level concepts in game theory. This time, I want to explore a couple of “games” that have substantially changed my thinking.

+ what I learned or rediscovered recently

* The prisoner’s dilemma

You may have heard of this one. Here’s the game:

You and a stranger have both been charged with a crime.
If you blame the stranger and they say nothing, you go free and they get 5 years in jail.
If the stranger blames you and you say nothing, you get 5 years and they go free.
If you both blame each other, you both get 3 years; and
If both of you stay silent, you each get 1 year for failing to cooperate.

In the best world here - for you at least - you get zero years in prison. In other words, you blame the stranger and they stay silent.

But of course, that’s exactly what they’re thinking, and they’ll blame you as well. So you both end up getting 3 years in jail. If only you could cooperate - and importantly, trust the other person - then you’d “collude” and both stay silent for only 1 year in jail.

The problem is that you can’t really trust the other person. If you trust them, and then they blame you, you get hit with 5 years in jail. Without this critical ingredient “trust,” you both end up with an outcome that’s worse for everybody.

Situations like these are surprisingly common in real life. If you’re offering to repair my car - but I can’t trust that you won’t take advantage of me - I probably won’t transact with you at all. Now we both lose. But if we trust one another, we’ll transact and we both win.

Trust is like a social glue that helps facilitate win-win situations. But trust can only be developed by playing cooperatively in long-term, repeated games - these are the games we should look for.

* The ultimatum game

This one is fascinating. Here’s how it goes:

I have $10.
I can give you any amount, between $1 and $10.
If you accept that amount, I keep the rest. If you reject it, we both get nothing.

How much will I offer you, and will you accept it?

A “fair” offer would be $5, in which case you get $5 and I keep $5. An exploitative offer would be $1, because I get to keep $9.

But you should prefer $1 to no money at all! If you are rational, you should be thankful you’re receiving any money - not concerned with what is “fair.”

So if we were both completely “rational” here, I’d offer $9 and you’d accept $1 and we’d both go on our way. Game over.

But let’s say you’re “irrational” - you’re just a liiiiiittle bit crazy. And you don’t care if you get $0 or $1 - you just care about things being equal.

Well you may reject my $1 offer, in which case we both get nothing. Suddenly now this is really bad for me: I could have gotten $9 but I now I get $0.

In other words, by not being totally “predictable” and “rational,” I can no longer take advantage of you. I just don’t know if you’ll blow the whole thing up. It’s like the kid in high school who had a bit of a crazy edge - you don’t mess with that kid.

The ultimatum game tells us we shouldn’t always be “rational.” Rationality is good, but not when we become so predictable we can be taken advantage of. Sometimes, we want to be just a little bit crazy!

* Keynesian beauty contest

Here’s the game:

There’s a beauty contest with 100 faces and 10 judges.
As a judge, you have to choose the most beautiful face.
If you choose the most beautiful face, you get a prize.

If you simply choose the face that you think is most attractive - well, the other judges may not agree with you.

You take a look at the judges. Who would they think is most attractive?

But not so fast! A better question is: who do they think the others are thinking is most attractive?

It goes meta real quick. What’s interesting here is that suddenly the notion of “beauty” here isn’t about your opinion, or their opinion, or anyone’s real opinion. It’s been completely detached from reality.

When we play games with other people - when we have to think about what they may be thinking - we can find ourselves in situations which bear little resemblance to reality. And when we get stuck in our own heads - or the heads of others - it becomes increasingly hard to separate fact from fiction.

Thanks for reading,