Hello, everybody. Here I'm back with another episode of my course, Experimental Economics
in Practice and in particular Programming in Z-Tree. The first, this very first section
of package two is nothing about programming. So if you don't like me talking about the
general ideas of experimental economics, then please skip this clip and continue with the
next clip. If you want to hear me talking about that stuff, then let's jump right next
into it. We are in package two. Congratulations, you survived package one. And as I said, in
package two, we first start with something that I would like to tell you about behavioral
economics. I assume that we all do not start from the very beginning, but that we have already
some certain knowledge about economics and also about behavioral economics. But I'd like to give
you an important message that results from me doing for quite a while, experimental economics
research. And I see quite often things, beginners in research in behavioral economics that do a
typical mistake that I'd like to avoid you. Let's start with a super simple example. This is
an ultimatum game with a shrinking pie. There are two people involved. And there is an alternating
offer right. So this is the very theoretical description of what we have. If we want to see a
concrete situation, it is that two people bargain, person A and person B. Person A, I'm sorry, has
to split 500 coins. If person B accepts, then the game is over. And the 500 points are split
according to the proposal of person A. If not, if B rejects, then B has the right to propose a split
of 250 points. So the pie shrinks. And then the same story applies to person A. So if person A
accepts this split, then the game is over and they caged off according to the proposal and
the rest goes to the other person. If A rejects, then we have another shrink pie of 125 points,
coins that have to be split between A and B. And then B has finally the right to accept or reject
that offer, the final offer from person A. If accepted, it's cashed off. And if rejected,
both get zero. Now, what is the optimal solution to that? You're not a beginner in economics,
so it's not difficult for you to compute that. You have to apply backward induction.
Backward induction means that at the third stage, so here, when A has to decide between
what offer to make out of 125, he or she offers person B, of course, one coin or the smallest
amount possible. Let's say it's one coin keeping the rest for him or herself. So B
accepts one coin and A gets at the last stage 124 coins.
And of course, this is anticipated by person B on stage two. So person B
gives person A one coin more than 124 points. That's 125 coins.
Keeping for him or herself, person B, 125 coins as well.
And of course, this, again, is anticipated by person A on the very first stage.
And at this stage, then person A gives person B one coin more than the 125 coins he or she,
person B, gets from in the second round. And that is 126 points. And at the end of the day,
at the end of the day, this means that person A gets 376 coins. So the optimal strategy for person
A is to offer in the first round 126 coins for the other person and implying that he or she,
person A gets 376 coins. So this simple, simple game theory, introduction to game theory.
Well, what is the problem?
What is the problem in terms of behavioral economics?
Well, we make very strong claims regarding the way people think about this problem.
Actually, I mean, this is very philosophical, but if there's an equilibrium, it is as people are
dead. There is no game. All the fun that we ask people is gone. Actually, when you
play that game here as an experiment and you do this, you want to get more insights about these
people. You ask, of course, person A what to do on stage one and on stage three.
But if there is, I mean, theoretically, there is no stage three at all. So why should I ask person
three, person B, A, sorry, for the answer of this third stage? Since we all know that there is no
third stage. So theory has a problem with reality. We all assume that when they solve
this whole thing, that they think in all in the same direction. So a specific direction of
sophistication. We all want to maximize our utility and we all understand that
my own income is the only source of my utility. And of course, this is a super strong assumption.
So actually, when we want to test behavior in the game, we basically play all the way
always with these two things. Actually, the experiment, if we run that experiment, it's not
about how you really behave in this game. Do you like 376 coins? But it's about the experiment
itself is about the way how people think about the problem and not really about the outcome.
So when we talk about insights that we have from the experiment, you should avoid saying,
oh, we know that people play off the equilibrium. So they gave 250, 250.
That is an outcome. This is an interesting outcome. Don't take me wrong. But the important
insight is, why do they take this outcome? So we relax those two assumptions and come up with a
theory that leads to this other result. The result is just the consequence of the other thinking.
And so be more focused on those two things here and how we relax that. Then if theoretically
relax that, then we are in the domain of behavioral economics and how to test that
relaxation that's experimental economics. And be more focused on those two things,
how to relax these things here, because this is the actual insight. It's an important
result that people in the automatum game play off the equilibrium. But the important insight is,
why do they play off the equilibrium? Not that they play off the equilibrium. So you want to
impose an experimental design that gives you more insight about why, then just to show that
they play off the equilibrium. So these critical assumptions, I already mentioned them,
not in a very straightforward way. So let us name them in the economic phrases. So narrow
self-interest is of course the tricky point here. If I play this game here
and my interest is not narrowly only on myself, on my own utility, but I draw a utility,
sorry not on my own income. If I draw a utility from harming you because you gave me a mean offer,
in the third round, this game becomes super rich and super interesting, not this dull
equilibrium analysis that I just mentioned before. So if we relax the narrow self-interest,
things become very, very rich and very interesting to analyze. But even if we have imposed
some trick, maybe you play this game with a robot, with a computer, then narrow self-interest maybe
makes sense. But nonetheless, now you can play around with the second element and that's the
common knowledge of rationality. That's our joint understanding that we follow the same
direction of sophistication. How people develop deeper insights about rationality
and the robot is a bit or the computer is a bit tricky because when I play with a computer,
I already assume that the other side is very rational and this is in reality when
people interact, it's I guess not the case. So think about good ways to relax those two things
and that gives you the powerful insights, not how we had a game and then they did not play the
equilibrium. And you have to be careful when you want to do that
because these game theoretic constructs, these elements that we are talking about,
they are very powerful. Here's an example of the evergreen. So the
ultimatum game just in a maybe more entertaining story with Ernie and Bert,
but who cares? So there's an ultimatum. And be aware that game theory is very powerful,
meaning that if you think, okay, I have a nice experiment and I can now work on this relaxation
of the two central things about behavioral economics, then game theory says, no, no, no,
you're wrong. It's just a matter of a different equilibrium concept. So I want to show you with
this little example here. So here's the entertaining story we have Ernie and Bert.
They want to steal 10 chocolate biscuits. Do they have the same mother? I don't know.
So the mother left the kitchen and it's only time to make one attempt to steal the biscuits from
the top of the board where she put the biscuits. But for that, the two kids, Ernie and Bert,
they have to cooperate. And it has to be that Ernie, who's always the more posh person to steal
and to more engaged in organizing some biscuits and some candy and stuff like that.
So Ernie has to climb on Bert's shoulder.
That means that Ernie has the biscuits in his hand. And so he has the right to make this proposal.
So he proposes how to divide the biscuits. And Bert can only agree or reject. And then if not,
the mother goes in, comes in, and games over. So this is the entertaining story.
And that's the game tree for that. Let's assume that Ernie, for whatever reason,
cannot make the proposal of zero biscuits, but between one and 10. And Bert can then
decide on how to respond to that, to accept or to reject. So we have the decision not Ernie
between one and 10. And then the decision not of Bert between accepting and rejecting all these
offers. And now how do we solve that game? Okay, backward induction.
Bert is going to accept everything. So now Ernie is getting this here. Sorry, it's
offering this, the lowest amount that is accepted. That's one and keeping nine for himself.
And that is the Nash equilibrium. Now you play the game and you find that people give five.
And that's your experimental insight. And then you say, oh, no, these two assumptions,
never self-interest or wrong. And then you're on the wrong track.
Because, oh, let's say that you find that people offer two, eight, instead of one, nine.
And you make sure that they all understood the game. Everything was fine.
Everybody was very rational. For some reason, you made somehow with a trick, you made sure
that everybody knew that everybody knew about the game, the rules of the game. And still you find.
Is this a violation of narrow self-interest? No. It's just the fact that there are other
non-subgame perfect Nash equilibrium in the game. Because this is a non-subgame perfect Nash equilibrium
of the game. Ernie says, I offer eight. And Bert says, I reject all the offers that are smaller
than eight and accept only offers that are larger than eight or eight. Well, because this
is a Nash equilibrium, because this is the best answer, the mutual best answer. So Bert rejects
all the offers smaller than eight and accepts all the offers. The best response of Ernie to that
is to offer eight. Because all the others smaller than eight is rejected. And then your
narrow self-interest utility, smaller, given that you offer less than eight.
Then if you give eight, when you give eight, you get two.
And otherwise you get zero. And so the birds, this is the best response. This is Ernie's
best response. Ernie's best response is to offer eight to this strategy of a bird.
And to accept eight is also Bert's best and response to Ernie's offer of eight.
So this is a best answer to a best response to a best response.
And this relies on this empty threat reject all offers smaller than eight.
But they are played, this threat comes from non-activated knots.
Now, why do I tell this story? This is not a course about game theory.
Well, if you want to show with experimental data that they don't
choice, their choice is not one eight, but their actual choice is five five or
two eight eight two, who cares, whatever. Then they just play a different equilibrium of the
game and it's not sub game perfect. And then the issue of your whole experiment is about
testing whether people play sub game perfect equilibrium or not. While you actually wanted
to attack the the narrow self-interest. So what you have to do instead if you have to collect
instances where people disagree and reject or you want to ask people and that is the important
message because rejecting is a clear violation in this game here, is a clear violation of
narrow self-interest. That is the important insight telling you, okay, we are not, we do not
think in the way of narrow self-interest in this game. Or you ask BERT to answer all hypothetical
questions. And then game theorists will say, but you know, they are non-activated knots.
So remember in this other game that I mentioned previously, it's philosophically questionable why
you ask people things that they will never ever see. So there are two experimental tricks.
Well, it's not really a trick, but if you observe violations, rejections, then you have clear
disprove of narrow self-interest. It's not showing that they play here, this knot is not
the violation, but some knots that is to this here. Or you ask them about the full vector BERT
and then sell your game theoretically in a shaky environment. Okay, so this is just a warning.
So people are very different, they are very heterogeneous and we are not there to claim,
oh, you should do this and that. So be careful when you criticize game theory,
because game theory, they are clever guys, these game theorists. So
try to follow the root of criticizing the fundamentals and not a different equilibrium
concept. And since people are so different and they may just follow different equilibrium
concepts because they are different in terms of their cleverness and so on and on, we all have
to take this into considerations. In other words, if you collect data about a person, remember what
we did in the first package, we played this public good game. And then we asked about,
yeah, in my last question of the question, we asked about the age. This means that
we have a three, a two-dimensional vector of these people and its contribution and the age.
Or if you ask people three times, then you have a three-dimensional outcome vector and you should
consider that. That means that you do not, if you play, let's say, if you play a public good
and before you play a lottery and your assumption is that people are risk averse and therefore they
do not contribute to the public good could be. And then it's not good experimental style
to report the mean risk attitude and then the mean contribution. Because
your outcome vector is two-dimensional, meaning that you have the risk attitude of your
of your participant and the public good contribution. And you have to consider both
at the same time. So are risk-loving people, how do they play public good and how do
risk avoiding people play a public good? In other words, zi, behavior in the public good,
conditional on xy. Yeah, so this is the important thing, the important insight. You may want to
start a paper with, this is the mean risk attitude and this is the mean contribution.
But the inside of your experiment is that you consider both dimensions of your vector at the
same time. Yeah, so if you have several parts in an experiment, if you run z tree, several programs
in z tree or in one program you asked about two dimensions, you have to consider them
at the end of the day when you make your analysis. There's also some nice literature on that on
two-dimensional or three-dimensional outcomes of new game and how you consider that.
I just wanted to mention that because I guess some of you are at the beginning of their PhD
and this is like a perfect booby trap for PhDs to run into that. So avoid
thinking in one dimension because then otherwise you end up with just testing whether the people
play a perfectness of an equilibrium. Okay, so I stop here and then we continue with the package