Alphas and Betas

This is not a post about dogs that dominate the others in order to expand their genes through the population. This is a post about UofA and Yale.

Last Sunday night I was chatting with a very good friend of mine. He said that this course online from Yale University on game theory is pretty good. So I watched the video from the first lecture.

I was writing the final exam of the econ200 class that I was teaching this winter while I was listening to the video.

At some point the Professor said this (minute 60):

Professor Ben Polak: So it could be that they think that this is actually--they haven't understood the experiment and they think this is a multi shot game, not a one shot game, good. What else could it be? What's the simplest explanation? What's the other obvious explanation? They could just be stupid, right? It could be., Are we allowed to say that in class?

Let's be honest here, when we say experiments in the real world in Game Theory--or the ones you read about in The New York Times--the real world when it comes to experiments in Economics really means undergraduates at the University of Arizona. I mean, I'm not making it up. It just does. They all are. I don't know anything about … are any of you from Arizona, I don't know. I don't know whether the average undergrad at the University of Arizona just has a sunny personality or whether they "spent too long in the sun." I just don't know which it is, right? We can't really distinguish from this.

How about at Yale. What's our numbers here. How about in this class? Do you want to mike your colleague here? So 238 at Yale--this is Yale--versus 36. So even at my level of arithmetic that's a lot less than 30%. That's more like less than 15%. It's about 15% I guess. So 236--I'm sorry 238--chose Alpha, and 36 chose Beta. Now there's one more lesson in this class and this is going to be it. This isn't the end of the class but one more lesson to take home. You guys are going to be playing games among each other today and until--whatever it is?--December 7, whatever is the end of term. Look around each other. You better get to know each other a bit. And what did we learn today about you guys?

[End of Ben Polak's words]

Ok. So let me explain what he did in his class and what I did in mine.

After listening that thing about UofA I decided to see if really undergrads here behave that way. On Monday I did the same experiment Ben Polak did in his game theory class. There are some huge differences in the settings of the two experiments:

1. His class is a game theory course. You expect that students enrolled in that kind of course have already taken some courses in economics that mention some concepts about strategic behavior. My class was an econ200 course, which here at UofA it is the very first course in economics for an undergrad.

2. Ben Polak did the experiment the very first day of classes. I did it the very last day of classes (the final was today, Tuesday).

3. Yale uses the system of grading with + and -. UofA does not use + and -, just A, B, C, D and E.

The experiment.

At the end of my class I presented a slide with the following:

The Grade Game

• Without showing your neighborhood what you are doing, write down on the yellow piece of paper (write your name) either the letter \alpha or the letter \beta.
• Think of this as a "grade bid".
• I will randomly pair your answer with one other answer.
• Neither you nor your pair will ever know with whom you were paired.
• Here is how grades MAY be assigned for this course:

And then after a few minutes I presented this second slide:

• If you put \alpha and your pair puts \beta, then you will get grade A and your pair grade D.
• If both of you and your pair put \alpha then you both will get grade C.
• If you put \beta and your pair puts \alpha, then you will get grade D, and your pair grade A.
• If both you and your pair put \beta, then you will both get grade B.

I gave enough time to think about the game before collecting their answers. I also remarked that this was NOT going to be the way to calculate their actual grade. Some people say that then they did not have enough incentives to play strategically, but in Ben Polak's class it was also remarked that this was only a game.

Results in econ200: 19 chose \alpha and 14 chose \beta. So that 57.5% chose \alpha.

It turns out that playing \alpha is the best you can do given that the other player is also maximizing her grade.

We have that
econ200 winter session UofA 57.5% chose \alpha.
Yale course on game theory for undergrads 85% chose \alpha.
UofA experiments (according to Ben Polak): 70% of undergrads chose \alpha

What happened? Is is true that UofA students have received too much sun? Is it important if the experiment is made the first day of classes or the last day? Would the results change if I said that this IS going to be the way of grading in the class? Notice that in my experiments the punishment is much stronger than in Polak's game (if me and my pair have different actions, one gets A and the other gets D, in Polak's class: if me and my pair have different actions, one gets A and the other gets C).

Note: Polak mentioned University of Arizona because this is the place where Experimental Economics began.