Chicken

From:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
To:  Hieram Luftweng [luftweng@econ.exemplar.edu]
Subject:  Chicken

Dear Prof Luftweng:

I would like to request an extension on my final project in your Game Theory class (Econ 110B) on the basis of utility.  In your syllabus, between item 9 on the iterated prisoner’s dilemma and item 10 on our class prediction market, you have a sidebar saying that students are expected to act in utility-maximizing fashion.

I know the syllabus also says a late project is an automatic fail, but I believe you’ll find that there’s greater utility for both of us at the point where you allow me an extension.

Best,
Malcolm

From:  Hieram Luftweng [luftweng@econ.exemplar.edu]
To:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
Subject:  Re: Chicken?

Malcolm-

The usual approach is to offer up some sort of excuse—illness, a dead grandmother.  I’m intrigued by your unorthodox game theoretical approach to extensions, but I’m not sure I follow.  Explicate.

-Luftweng

From:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
To:  Hieram Luftweng [luftweng@econ.exemplar.edu]
Subject:  Re: Chicken??

Prof Luftweng:

I’m gratified that you find my approach intriguing!  Here it is in more detail:  a game of chicken.  We drive directly at each other at top speed until one of us swerves, or we die in a bone-crushing collision!

Here it is in greater detail still:  as you told us in the relevant lecture, the winning approach to a game of chicken against a rational opponent is to remove your steering wheel.  I have done so:  I have precommitted to file a complaint with the Dean if I fail this class.  I gave the complaint, pre-written and signed, to a friend, who I have instructed to deliver it if I am not given the extension.  The friend will destroy it if I am given the extension, and will listen to no further instructions from me in any wise.

Dealing with a late assignment is a nuisance, but I believe dealing with the Dean’s office to be a much greater nuisance.  Let’s assign the numbers as follows:  you will get -15 utility for failing me and having to deal with the Dean, and -2 utility for having to grade a late assignment.  In my experience, these numbers accurately describe the nuisance of extra work versus the nuisance of bureaucracy.  It’s clear in any case that your loss of utility is smaller in granting me the extension than in failing me.

Best,
Malcolm

From:  Hieram Luftweng [luftweng@econ.exemplar.edu]
To:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
Subject:  Re: Chicken???

Malcolm-

I have dealt with the Dean’s office before, and your numbers are accurate.  However, the trouble with the steering-wheel removal analogy is that I have already removed mine.  The note in the syllabus that I will fail any late final projects is, in effect, a steering-wheel removal.

But please continue to unpack.  How would you assign your own utility gains or losses?  Do you have a payoff matrix?

-Luftweng

From:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
To:  Hieram Luftweng [luftweng@econ.exemplar.edu]
Subject:  Re: Chicken????

Prof Luftweng:

It’s only a steering wheel removal if the steering wheel is actually gone!  Lifting your hands from the wheel and saying you won’t touch it just doesn’t suffice.

Whatever it says on the piece of paper you gave us at the start of term, the final grade is at your discretion.  There’s no credible precommitment here.

As for my own utility, let’s see.  If I fail the final project, I fail the class and will have to retake it.  This is a significant loss of utility for me.  Let’s call it -50.  And I’ll gain peace of mind and a good night’s sleep if I receive the extension, and will likely improve my grade in other classes.  Let’s call that +5 utility.  Here’s the payoff matrix.  You can see that it’s significantly better for both of us if you give me the extension.

Best,
Malcolm

From:  Hieram Luftweng [luftweng@econ.exemplar.edu]
To:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
CC:  Amy Maxwell [amaxwell@exemplar.edu]
Subject:  Re:  Chicken!????

Malcolm-

But you haven’t finished your matrix—where is your own decision regarding whether to sleep or actually do your work?  Consider this a professorial chiding.  Here’s the payoff matrix as it ought to look.

Ah, perhaps I should mention.  I know which friend you’re talking about, and am, through this email, letting her know that if she delivers your note, she will get a barely passing grade in this class.  That is, low enough to upset her parents, not low enough to have cause for complaint with the Dean.  I have given you back your steering-wheel.

Now—are you entirely certain this is still a game of chicken?

-Luftweng

From:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
To:  Hieram Luftweng [luftweng@econ.exemplar.edu]
Subject:  Re: Chicken?!???

Prof Luftweng:

It is a game of chicken, but one in which there is no reason for you not to swerve!

The standard game of chicken looks like this:

You’ll note that in the standard game, my swerving and your going straight gives you a modest payoff.  You look macho and I look weak, but nobody dies.  In our version, though, there is no reason for you to go straight!  If I swerve by finishing the project on time, it doesn’t matter whether you give me the extension:  there is no difference between the lower left and upper left corner.  Given that, the most sensible strategy for you ought to be swerving, since you can’t be sure I won’t go straight:  in fact, whatever you might have convinced poor Amy of, I at least tried to credibly precommit to do so!

Best,
Malcolm

From:  Hieram Luftweng [luftweng@econ.exemplar.edu]
To:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
Subject:  Re:  Chicken??!??

Malcolm-

Again, you have failed to consider something important.

As with the prisoner’s dilemma, an iterated game of chicken is different from a one-off.  In a one-off game, in which you are credibly precommitted to sleeping, it makes more sense for me to maximize my utility by choosing to give you the extension.  And for you, this is a one-off game.

Not so for me.  If I choose to grant you the extension, then I should make the same choice again given the same situation in the future.  I teach this class every semester.  My payoff looks like this.

The frowny face represents my life once enough students figure out the approach you’re using here.  There is only one way to avoid being buried under an ever-increasing heap of negative utility, and that is to avoid the scenario entirely by precommitting to fail any student who turns in a late final project.

It’s on the syllabus.

-Luftweng

From:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
To:  Hieram Luftweng [luftweng@econ.exemplar.edu]
Subject:  Re: Chicken???!?

Prof Luftweng:

It doesn’t have to be an iterated game of chicken!  I will precommit to never telling another student the outcome of this one.  I have a contract ready to hand over to you, saying that should I renege on my commitment and tell other students, or should I try to invoke the game of chicken with you again, I owe you a sum of money equivalent in net present value to the utility I gain in getting the extension.  You can specify the currency to utility exchange rate, if you like.

Or, would you prefer some compromising photographs of me?

Best,
Malcolm

P.S.  On a related note, the point of the final project is to prove that we’ve learned the material, isn’t it?  To show that we’ve really mastered game theory and utility and so on.  I feel that our conversation here shows I have a strong grasp on the material.  Would you agree?

From:  Hieram Luftweng [luftweng@econ.exemplar.edu]
To:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
Subject:  Re:  Chicken!!!!!

Malcolm-

And now we come to it.  The moment where one of us swerves, or we collide.

To some people, the argument you have laid out would be compelling.  They would agree with all of your points, would lay out the numbers, and would make the choice of greater utility in granting the extension.  This type of person, the naïve utility-maximizer, will naturally attract loaded games such as your game of chicken.

In order to prevent people from giving me loaded games, i.e. in order to be the type of person to whom, in general, people will not present loaded games, I must reject your loaded game.

Your P.S. is correct.  You have demonstrated a strong knowledge and mastery of the material, above and beyond what I normally expect of students in my class.

You fail.

-Luftweng

From:  Malcolm Gorlitz [mgorlitz@exemplar.edu]
To:  Hieram Luftweng [luftweng@econ.exemplar.edu]
CC:  Amy Maxwell [amaxwell@exemplar.edu]
Subject:  Class Prediction Market

Prof Luftweng:

Not a problem, and thanks for your time.

A month ago, I placed a bet in our class prediction market that I could simultaneously convince you that I knew the material, and convince you to fail me.  The payoff is that Amy will finish up my final project.

Boy, this email exchange really gave me a much more concrete grasp on the material.  You should do this sort of thing more often!

Best,
Malcolm

P.S.  So listen, I’m applying to law schools starting next month.  Would you like to write me a letter of recommendation?  I’ve got a great argument for how that would maximize everyone’s utility!

2 thoughts on “Chicken

  1. Originally written: last week
    Edits: minor
    Group theme: “The Things Unfinished”
    Inspiration: too much game theory reading (in particular, a post about excuses by Scott Siskind)

  2. What a pleasure to read: it’s well-written, funny, and undersranding it makes me feel oh so terribly clever :)

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