Econ 223 Midterm Exam September 8 2003
120 minutes (2 hours)
i've
included some suggested answers here JF 2004
Closed book exam: no notes, no books, no cell-phones, no calculators just you
Make sure your answer appears in the workbook with your name and signature on the label
There are 4 short answer questions (18,40, 22 and 20 marks each) for a grand total of 100. Answer all questions in the answer booklet provided. Please make sure your name, signature, and student ID are printed clearly on your answer booklet.
Question 1 [18 marks] :Dixit and Skeath (DS), the author's of the textbook for the course, classify games into a number of various "pure types" by asking and answering some interesting questions. Identify these types and briefly explain the key concepts/distinctions used to interpret and understand each type. (By "briefly" I mean in no more than 1-2 sentences per key concept; you do not have to provide example games in your explanations.)
Question 2 [40 marks in 4 parts] Virgin Air (VA) is deciding whether to enter the market for air travel services within New Zealand and between NZ and other Pacific countries. Suppose we take a step back in time where Virgin Air hasn't yet decided whether to enter this market (ENTER) or to stay out (STAY OUT). A very real strategic problem is that Air NZ and Quantas may integrate their management and ownership structures. Suppose this merger is permitted in some form or another and that the new merged airline is called Quanza. If VA stays out of the market it doesn't earn any profits here in NZ, and Quanza has an effective monopoly earning $100 million for the first year. If VA decides to enter, Quanza has to decide a pricing policy by keeping prices at a moderate level (Pmod) or engage in an all out price war with Virgin Air (Pwar). A moderate pricing policy means each will share the market, albeit without a monopoly. Suppose the bigger firm, Quanza, earns $50 million and VA earns $30 million in net profits under a moderate pricing policy, but that if an all out price war occurs each firm loses $20 million . Assume for this question that only the $ payoffs in the first year matter.
2a) [12 marks ] Draw and label the game tree for this sequential game. Use "pruning" to identify the rollback equilibrium.
2b) [3 marks] How many pure strategies does VA have? How many pure strategies does Quanza have?
2c) [15 marks ] Represent the sequential game of part "a" as a simultaneous game using the players' strategies and the payoffs associated with each combination of pure strategies to develop a payoff matrix. Put Virgin Air as the Row player and Quanza as the Column player and represent payoffs in the conventional manner for game theory. Find the pure strategy Nash Equilibria of this simultaneous form representation of the game, if any, and use game theory to explain the relationship between your answer(s) and your answer to part "a" .
2d) [10 marks ] Suppose the timing and information structure of the game is changed so that Quanza moves first by announcing its pricing policy, then Virgin Air moves next deciding to enter or stay out. Draw and label the game tree for this new sequential game. Use "pruning" to identify the rollback equilibrium and compare your answer to your answers to "a" and "c".
click here for a suggested answer
Question 3 [22 marks]The table below represents a 2 player simultaneous game with payoffs in dollars indicated in standard fashion:
|
Column |
|||
|
Row |
L |
M |
R |
T |
3,0 |
4,7 |
6,4 |
|
L |
5,4 |
2,2 |
12,3 |
|
H |
2,3 |
3,1 |
10,2 |
|
B |
4,5 |
5,6 |
8,7 |
3a) [3 marks] Does either player, Row or Column, have a dominant strategy?
3b [12 marks] Solve this game using the method of iterated elimination of dominated strategies. Explain your steps briefly.
3c) [7 marks] If the payoffs in cells T,R are changed from (6,4) to (9,4) and payoffs in cells L,L are changed from (5,4) to (3,4) what kind of standard game is the new game most like: assurance, tennis/lineout, battle of two cultures, prisoner's dilemma, battle of Bismarck sea? Explain briefly
click here for a movie answering this question 
Question 4 [20 marks]TaxPayers and Inland Revenue (IRD).
JF COMMMENTs
in 2004 readers -this question was too tough - as explained in the
accompanying video - so
you don't need
to worry that something as tricky as this will be in the 2004 exam. BUT
drawing the game tree and being able to give a descriptive qualitative
analysis should be a piece of cake by the time you do the course
Businesses and self-employed persons have to fill out annual tax returns. These tax returns always ask the taxpayer to sign a form declaring that they have truthfully represented their net income situation. While taxpayers may report all expenses honestly, regrettably some have been known to lie about business or employment expenses, eg travel, meals, accommodation, computers, etc. Was expense item "A" really for business or for personal use? Also, the tax authorities can simply accept any tax claim (AC for Accept) or they can audit or inspect taxpayer claims (AU for audit). If an audit is conducted it costs the IRD $4 in resources of their time and money and the taxpayer $2 in resources of her own time and money, so other things equal no-one really wants to audit. But other things may not be equal, and the tax authorities don't want to lose out on tax revenue that should be paid. Whether any particular expense item is a legitimate claim or not is private information to the taxpayer at the time she is filling out her return. The tax authorities can audit (inspect) taxpayer claims, and lets say that with enough effort the IRD will find false claims for sure. But they have to make that decision after they receive the taxpayers claim and not knowing whether the underlying expense is really legitimate or not without auditing. (You may assume that there are no other penalties for filing illegitimate claims in this part of the question).
Suppose that "Nature" a fictitious player, makes the first move in the game: with probability 1/2 Nature selects either a legitimate (LEG) or an illegitimate (ILLEG) expense item, and this 50/50 probability assessment is common knowledge to both taxpayers and tax auditors. Suppose also that the expense item is worth $10 in tax revenue savings to the taxpayer. Next, the taxpayer observes her expense item privately and decides to either claim it as legitimate or effectively "say" the expense item is not legitimate by not claiming it on her tax return.. You may, and should, assume that if the expense is truly legitimate that taxpayers will never say it is not Ðthey always claim legitimate expenses as deductible. But when taxpayer gets a personal expense from Nature that they know the law would regard as illegitimate, the taxpayer has a choice to either tell the truth and not claim the expense, ie "SayILLEG", or lie about a particular expense item and claim it as a business expense, "SayLEG" .
Note: you may find parts 4c and 4d more difficult than 4a and 4b Ð they are worth only 8 marks in the exam so don't let yourself get "rattled" if you're having trouble.
Q4a [10 marks]Sketch and clearly label the extensive form for this sequential game.
Q4b[2 marks]How many pure strategies do Taxpayers have in this game? Describe them.
How many pure strategies does the IRD have? Describe them.
Q4[c][3 marks] Construct a payoff matrix for a simultaneous game representation of this game. Match up each and every pair of strategies in your answer to Part 4b, one from the strategy set of Taxpayers as a Row player, the other from the strategy set of the IRD as a Column player, and put the payoffs to each player in each strategy combination in the appropriate cells of the payoff matrix. You will find that the payoffs to any particular player depend on what Nature does: so use the probability weighted average idea to calculate the "expected" payoffs to each player. If you are unsure about the accuracy of your algebra write down the formula or method you are using to calculate the relevant probability weighted average.
Q4d [5 marks] Analyze the game using the Nash equilibrium concept to develop a prediction for the strategies and payoffs players will use in this game. Start with pure strategy Nash Equilibria ideas first. If you need to use mixed strategy ideas in your explanation explain why. If your math abilities leave you "algebraically challenged" so that finding precise mixed strategy equilibria is not your strength, then please be advised that a reasonable written explanation will get as good a grade on this portion of the question as a well explained precise mathematical calculation.
check this suggested answer out for number 4 click here