• Matin K.
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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 player 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 done that 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 greater than 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 what’s 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 are 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 www.gurume.co.uk. The link would be in the description below.