Hi guys, I’m Matin, I’m a second year
Economist at Cambridge.
I’m going to give you an idea of the kind
of question you might get at an Economics
interview at Oxbridge.
So it begins as follows with the following
question.
I give you a 100 pounds you must offer part
of it to someone.
If they reject the offer, you get nothing.
How much do you offer?
So it’s actually quite a straight forward
question to begin with.
If any of you have done elementary games theory,
then you will recognize this is the ultimatum
game, dynamic game which is set up as explained.
Basically, your aim is to maximize how much
you get and obviously there is a trade-off
between how much do you offer and then there
is a risk of them rejecting you.
So the main standard approach is to begin
with the basis of rational choice theory.
This assumes that each agent you and the other
agent are perfectly rational.
They are simply trying to maximize their monetary
pay-off.
So how much money is there altogether?
So we have £100.
We are going to assume this.
The smallest division of money is a single
pence 1 pence.
You could just assume 1 pound maybe they might
tell you in the interview what to assume.
So you are going to assume 1 pence.
So the game can be modeled as follows.
Now if you’ve heard of the game, you might
already know the conclusion.
If you haven’t then like much of economics,
you can work it out with a bit of common sense.
So I’m going to model the game in what might
appear a little excessively complicated to
begin but you will see what I do in a moment.
So because of the dynamic game, I’m going
to draw a tree and it’s going to be as follows.
I’m going to draw a cone to represent: this
is player 1’s decision node I’m going
to draw a cone to represent all the possible
offers that player 1 could give and denote
any given offer as x.; x being what player
2 receives.
Ok so here we have player 2 pay-off as x and
100 minus x as your pay-off.
Clearly this is what you are trying to maximize.
It makes intuitive sense that what you receive
is 100 which is the total amount subtracting/minus
the amount you offer.
This is your decision; this is how much you
offer.
Then player 2 has to make decision whether
to accept or reject the offer that you give
them.
So either if they choose to accept in which
case your pay-off is 100 minus x and they
of course receive x.
Alternatively say they reject, then you will
receive nothing, you will both get 0 pay-off.
Now if we are going to assume perfect rational,
then it clearly seems the answer to this,
if we are going to work backwards (so this
is asking how you will solve dynamic games;
you work backwards), then clearly player 2
being rational will always accept your offer
so long as x is non zero.
So long as x is greater than 0 and knowing
this, it seems very obvious what offer you
should give.
If x is always going to be 0 you want to maximize
100 minus x, you should offer 1 pence so x
equals (if we are going to work in pounds,
I’m going to say a 100 is a pound) x should
equal 0.01, giving the player 2 pay-off of
x and giving you a pay-off of 99 pounds and
99 pence.
So this conclusion that x equals 0.01 that
the offer is you should give is 1 pence is
also known as the sub game perfect nash equilibrium
or alternatively in this case the backwards
induction equilibrium because as you just
saw we solve this game working backwards.
So we found out what’s player 2’s strategy;
what’s his best response to whatever you
do and worked out that that’s actually accepting
the offer so long as x is greater zero.
Given that, what do you do?
Well, you decide to offer o.o1.
So you could just stop there but when you
think about it actually if you are given a
hundred pounds and you had to share with another
real life person, would you follow the advice
of this model and actually offer 1 pence?
Well, chances are you won’t and you probably
shouldn’t either because actually a lot
of the experimental evidence surrounding this
game done on the ultimatum game suggests that
this is not the case.
It doesn’t happen.
This isn’t a legitimate equilibrium; and
actually around offers of 30% or less is normally
rejected.
Okay, so in that case, what is the reason,
are we even playing the ultimate game?
What should you actually offer going back
to the question.
So this really goes back to our assumption
of rationality, we are assuming that the other
player only cares about their monetary pay-off.
As such, they will accept any offer which
is strictly positive.
But in reality, people often exhibit other
preferences wherein known as social preferences.
For example they may care about the division,
the share, this difference between the 100
minus x and x.
They actually care about the difference.
It might be what’s called inequity averse,
equity conscience.
They care about how much they get relative
to you and that if they perceive the share
to be unfair they will reject.
Alternatively, you might/ you don’t know
whether they have that preference or not but
because you fear they could you decide to
give him an offer which is higher precisely
because of the idea that they might have that
preference.
Alternatively, they might have preference
known as reciprocity which means that they
assume that there is some social norms, some
basic level of fairness that you will engage
in, that you will give a certain close to
50:50 offer and that if you don’t that you
will be punished for it even though it will
mean that they will end up with a lower monetary
pay-off.
They may feel more satisfied punishing you
than any small amount of monetary pay-off.
There are various extensions to the ultimatum
game and various variations which they may
or may not explore in the interview.
For example, there’s one simpler game which
is called the dictator game and actually there’s
no second stage.
You simply give an offer.
They don’t have a choice to reject and it
has to accept whatever you give (known as
the dictator game).
Actually evidence surrounding that game lends
some more support to the idea that actually
people are acting rationally because it’s
found that offers are generally much lower
in the dictator game.
They don’t fear reciprocity.
From player 2, they don’t fear being punished.
So generally offers are lower.
However there is also evidence against that
conclusion, people still being equity conscious
in their decision to, in the offers that they
give.
Another variation is called pirate game.
It is basically the ultimatum game but with
5 players instead of just 2.
Conclusions to these are often very interesting
and contrast a lot with what you would intuitively
believe to be the result.
Okay, so I hope I gave an idea of what to
expect at an economics interview.
I think hopefully I showed that often the
questions can start off sort of simple; perhaps,
you even heard of it as bonus.
But if you haven’t, there is no need to
worry.
You just have to read the question more carefully.
Really ascertaining what they actually want
from you and then to explore that.
Often in an interview, if they have this kind
of question, they will develop it.
So for example, in the question we just had,
there are various ways they may have progressed.
They could have looked at other games, developed
the actual game; perhaps looked at experimental
evidence.
Usually, they don’t do all of these but
some of the things.
But the main thing I think to take away is
that once after you have read the question
very carefully and you know what it is they
want from you is to not necessarily to take
the question for a face value.
So for example, this question asks how much
do you offer.
But then, it didn’t say “How much do you
offer given that you want to maximize your
monetary pay-off?”
It’s actually quite an open question.
For all you care, you are equity conscious
and you would do 50:50 because you would feel
bad you know.
You could tell the interviewer this and explain
your reasoning why and that’s not something
they disregard; in fact, that would help give
insight into the actual question as we saw.
It helped to explore social preferences and
this idea.
So definitely questioning the underlying assumptions
of the question is something I recommend after
you’ve had a bit of time to think about
the question itself.
So if you would like more information about
applying to Oxbridge or your application for
economics or any other subject, definitely
check out gurume.co.uk.
The link would be in the description below.
