2018 Exam question, with suggested answers

Last year I also published immediately after the exam, and one student complained that knowing the answers to my exam disrupted his/her preparation to the other exams, and that I should have published my answers only at the end of the exam session.

If you have the same attitude as this student don’t click on the link. If you want to see the answers, they are available here.

I shall NOT answer any further email or make any further entry on this blog, until the results are officially published.

 

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Break a leg

Or, “in bocca al lupo”, as we say in Italy.

If you have done your work you will do well. Remember, READ the QUESTION. And answer the question.

Also assign your time before you start, and keep an eye on it. Every year there is always someone who write two lines, and then, sorry I run out of time. I cannot mark what you have not written.

Recall the exam has three Sections, of equal weight. Section A will require to answer all the questions, Section B and C will give you a choice of one out of three questions.

If I with all my accumulated wisdom, were to sit the exam tomorrow, I would devote 15 minutes to reading the whole paper carefully (yes, 15), then 30 minutes to each Section, and keep 10 minutes for checking your answers.

No more posts today. I shall post suggested answers tomorrow, after I collect the scripts (around 3pm).

 

Extensive forms games

Hi Gianni,

I know you have already gone over the question but could you explain how to find the nash equilibria on question 6 2015-16 paper. 

Thanks

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  1. Identify the subgames There are two starting at nodes 1 and at node 7.
  2. Find the NE at each subgame
  3. For each Nash Equilibrium of the whole game (that is of the subgame starting at node 1 ) induces a NE at the subgame starting at node 7.

In other words, C must choose RC at node 7. Given this, B cannot do better than choosing RB at node 3 and Alfie cannot do better than choosing RA. Symmetrically for { LA, LB , LC}.

There are other SPE, but they can be ignored, though you would not lose marks for mentioning them.

Simple arythmetic

Hi Gianni,

 With reference to Part 6, Slide 46 (Quantity Competition: An Example), for maximising total profits, I got the correct output from my calculations (A/6 each) but my profit is coming up as (A^2/6), I’ve tried repeating it several times but can’t seem to get it right.

 I think I may be missing something, could you explain how that value is reached?

 Thank you!

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I get the right numbers: a firm’s profit is (A-A/6-A/6)A/6 – A^2/36 = A^2/9.

Strategies in extensive form games

Hi Gianni,

I know you have answered various questions on this question before but there is still one thing I am not too sure of. In the 15/16 paper, in question 6 (the one based on choices between London and Rome) Why would Cynthia’s strategies be (LC,LC) (LC,RC) (RC,LC) and (RC, RC)? You have previously mentioned that the mock answers have a mistake in that Cynthia’s choices are infact LC, RC not LB, RB that is just a mistake, but I do not understand why doesn’t she have four choices i.e one at each node 4,5,6,7. i.e why would her choices not be (LC,LC,LC,LC) etc rather than just (LC, LC) since she must surely have four choices to make rather than two?

Thanks

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A strategy in an extensive form game is a combination of choice of action at each node, with the additional constraint that the action must be the same in every node of each information set.

This can be shortened as “a strategy is an action at each information set”

In the specific example, Cynthia may know that she has reached one of nodes 4,5,6 but cannot tell which of the three nodes she is at. Imagine that she phone the travel agency, and asked “Did both Alfie and Bob book tickets to Rome?”I if the answer is Yes, she is at node 7, if the answer is NO, she can be at anyone of nodes 4,5,6: she must take the same action at these three nodes, because she does not know at which nodes she is.

On the number of questions in the exam

Dear Gianni, 

 I have a quick question. I am just wondering as this will be the first paper set by only you this year, how many questions will there be in each section. will it be the same as previous years where it was 2 in section A and 3 in section B and C? I am asking this as it will allow me to prepare to manage my time appropriately for the exam. 

 Thanks, 

====================

As I said, there will be three Sections, of equal weight, Section A will require to answer all the questions, Section B and C will give you a choice of one out of three questions.

The number of questions in Section A depends on the examiners assessment of the time it should take to answer. I some past exam papers there were more than two questions, though some were groups together under the same general number.

As a rule, devote 15 minutes to reading the whole paper carefully, 30 minutes to each question, and keep 10 minutes for checking your answers.

Solving simple games

Hi sir,

Thanks for taking time to answer our questions. I have been through the slides multiple times and am confident on finding the correct mixed strategy equilibrium for a game, but the one thing I am not sure on is how you know when you need to check if there is a mixed strategy? Or if there is a certain way of knowing if there is or isn’t a mixed strategy. In one of your papers you mentioned that for one game theory question numerous people tried to find a mixed strategy and couldn’t find it (because there wasn’t one) so I wanted to know if there is a way to avoid this by knowing when or when not to test for a mixed equilibrium? Thanks

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I have given a couple of theorems which help: (i) a Nash equilibrium exists: thus if you find no pure strategy equilibrium, there must be one in mixed strategies (ii) an equilibrium in dominant strategies is unique (and is obviously in pure strategies). So if you find one it means there cannot be an equilibrium in mixed strategies.

Other that that, you could use the rule of thumb that coordination game often have mixed strategy multiple pure strategy equilibria, and also a mixed strategy equlibrium (think battle of the sexes).