September 09, 2004

How I Presented the Prisoner's Dilemma

I didn't have time to get human subjects permission before I started teaching (and I'd like a word with you about this Mark), so I decided to try to introduce the Prisoner's Dilemma without making the students think they had anything at stake in it. I've found/heard that one big problem is getting across the idea of a dominant strategy. So here's what I said (hyperlinks not in original):

Let's say you're playing a game like rock-paper-scissors, but with two choices: Thumbs up and thumbs down. You're playing against a blob; each of you simultaneously puts your thumb up or down without seeing what the other one does.. [Later I had to explain that the blob has thumbs.]

But you're not trying to beat the blob. All you're trying to do is to get the maximum payoff for yourself. And you don't care whether the blob does well or poorly--it's just a blob, you don't care about it at all.

I'm going to show you what you get for each of the possible choices:

It chooses Thumbs up Thumbs Down
You choose
Thumbs Up +2 -1
Thumbs Down -2 +1

Do you know what you should choose? Who thinks you should definitely choose up? Who down? Who doesn't know?

One person said "up"; I said that these were all going to be trick questions, but it's OK to be fooled by a trick question in philosophy because you'll get to change your answer.

If you said you didn't know, why not?

"Because you don't know what the blob will do."

OK, now let me fill in the blob's payoffs [underlined]:

It chooses Thumbs up Thumbs Down
You choose
Thumbs Up +2 -4 -1+3
Thumbs Down -2 -2 +1+5

What will you choose?

"Thumbs down."


"Because you know it'll choose thumbs up."

Good. Now let's try this again with a new payoff matrix for you:

It chooses Thumbs up Thumbs Down
You choose
Thumbs Up +2 0
Thumbs Down +3 +1

Do you know what you'll choose?

"Thumbs down."


"If you choose thumbs up you could get nothing."

OK, but what if it chooses thumbs up and you choose thumbs down?

"You still do better by choosing thumbs down."

About here someone said, "So is this basically the Prisoner's Dilemma?" We'll pretend that didn't happen.

So do you have to know what it does before you decide to choose thumbs down?

"No. No matter what it does you're better off choosing thumbs down."*

Now I'll fill in its payoffs.

It chooses Thumbs up Thumbs Down
You choose
Thumbs Up +2 +2 0+3
Thumbs Down +3 0 +1+1

Now what will it choose.

"Thumbs down. It can think the same way."

So it seems only logical for you to choose thumbs down, and for it to choose thumbs down. And you each get one point. But if you'd both done what seems illogical, and chosen thumbs up, you'd both have done better.

Then I try to give some more real-life examples, and later connect it up to Hobbes' analysis of the state of nature.

*For some reason I can't find a good link for "Good ol' rock. Nothing beats rock." [UPDATE: That's because it's "Good ol' rock. Nuthin' beats that"; I added this link to the main text, and here's the condensed script; thanks to commenter Blar.]

Posted by Matt Weiner at September 9, 2004 01:49 PM

Kramer- I thought paper beats rock.
Mickey- Na rock flies right through paper.
Kramer- What beats rock?
Mickey- Nothing beats rock.

And on the next couple turns, they both go with rock.

Rock, Paper, Scissors... Rock, Rock.


Posted by: Kramer Fan at September 9, 2004 03:29 PM

Sorry, Kramer Fan. That was a good one, but I think that he's referring to this:

Lisa: Look, there's only one way to settle this. Rock-paper-scissors.

Lisa's brain: Poor predictable Bart. Always takes 'rock'.

Bart's brain: Good ol' 'rock'. Nuthin' beats that!

Bart: Rock!

Lisa: Paper.

Bart: D'oh!

Posted by: Blar at September 9, 2004 11:20 PM

Kramer Fan, that looks like a cool link, but Blar is right--I was thinking of the Simpsons. And the reason I couldn't find a good link is because I was searching on the wrong quotation. D'oh!

Posted by: Matt Weiner at September 11, 2004 02:32 PM