University of Canterbury Economics Department

Midterm exam for Economics 223:March 27, 2006

with suggested answers and comments JF

here is the histogram (frequency counts) for the overall exam and for each question. The average mark (62) is slightly higher than in previous years (approx59-60) .

When you collect your exam script check the numbers for each question and the total to see that they match up with what I have recorded for you (published here in a table by student ID). Please let me know of any discrepancies.

On the multi-part questions I typically write an answer as "X+Y". Eg question 2 "8+0" was a frequent mark, the first part was worth 8 marks and the second part worth 6 marks, so 8+0 means 8/8 for part 1 and 0/8 for part 2. On question 4 a typical mark would be 10+8+6; the first part is worth 10 marks, the second part 8 marks, and the last part 12 marks (equally split between the correct analysis and the explanatory comment): here 10+8+6 means full marks on parts 1 and 2 and 6/12 on part 3.

You have 2 hours for this exam. You may leave any time after half an hour has elapsed. It is a closed book exam -no notes or books in written or electronic form are to be used. Please make sure all cellphones and electronic clacluators are turned off - failure to do so will mean confiscation of your exam script. Please answer all questions in the exam booklet provided. Please make your writing legible - I won't mark what I can't read.

Question 1            18 marks        Dixit and Skeath game types
Question 2            14 marks        Reality TV strategies
Question 3            10 marks        Counting strategies
Question 4            30 marks        AIDs pricing in Less developed countries
Question 5            28 marks        4x multi choice

Question 1  (18 Marks)  Dixit and Skeath (DS) 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; you do not have to provide example games in your explanations.)

answers: see previous midterms... Generally this year most people heeded my advice and did their homework for this question.

Question 2: (this question has 2 sub-parts) . Jack and Jill are playing a simultaneous one-shot game for a reality TV show. Jill starts in Auckland and has an envelope with four airplane tickets to four different cities (New Plymouth (NP) , Napier (NA), Nelson (NE), Queenstown (Q)} ; Jack starts in Christchurch and has four tickets to the same four cities in his envelope. They each know that the other player has the same destination airline tickets, but they cannot communicate with one another. Jack and Jill each have to choose ONE city from their list, simultaneously and independently, travel there using the ticket provided, and if their choices match up and they arrive in the same city they will each receive a payoff of $5 thousand dollars.
2.1 Draw the payoff matrix for this game and clearly identify (by circling relevant cells) the Nash Equilibria in pure strategies…or explain why there are no nash Equilibria in pure strategies.

2.2 Assume Jack and Jill do not know one another at all, but that otherwise they are rational intelligent players, and that each knows the other is rational and intelligent, and each knows the other knows that they know...etc...What key idea in game theory can you use to predict the outcome of their interaction (explain briefly, ie in a paragraph or less).

The problem is one of pure coordination with multiple nash equilibria (ie multiple reasonable self confirming beliefs to have) . The players might be able to find a focal point to bring about a convergence of expectations. One possible focal point that makes one strategy "different" is that all of the cities except one, Queenstown, start with the letter N - ie it is obviously different. This is obvious if one sketches the payoff matrix as i have...but if Jack is reasoning this way it also has to be obvious to Jill too , and Jill has to think it is obvious to Jack that it is obvious to her...If some kind of focal point reasoning cannot be used to bring about a convergence of expectations then, alas, anything could happen. Some students suugested some point halfway in between, like nelson - fine, but for full marks you needed to have some recognition of the focal point problem here....that these intelligent players recognize the

Question 3 Count Strategies The following game tree represents a 3 person sequential Game. How many stratgeies does each player {A,B,C } have in this game?  List the strategies for player B. (you do NOT have to list the strategies for the other players). 3x3=9 for A,2x2x2=8 for B (ttt,tbb,btb,bbt,ttb,tbt,btt,bbb} , 3x2=6 for C; as you can see from the histogram many many people are not counting these strategies appropriately...which makes me think i haven't taught you very well how to do this. If you answered incorrectly can explain the logic of your thinking to me on webct i'll try see if i can figure out where and how your logic is incoerrect...so you can better identify stratgeies in a game.

Question 4: Pricing AIDS drugs in Less Developed Countries (LDCs) .(this question has 4 parts and is worth 30 marks ) Millions of people in LDCs have died prematurely of AIDs and its' opportunistic infections in spite of the fact that there are combinations of modern drugs which, if taken regularly, can extend both the quality and length of life for HIV+ infected people. Technically the drugs are "available" to infected people in LDCs - but only at the same high prices that they are available in wealthier western countries like Amercia or Europe. But how can someone with income of $25 a year afford a drug that is priced at $10,000 a year? Multinational pharmaceutical companies (BigPharma) say they would gladly lower prices for AIDS drugs in LDCs if those countries would impose and enforce restrictions on the resale of those drugs back in wealthy countries like Amercia or Europe. But if BigPharma did actually price AIDS drug low enough to make them affodable to the LDCs, people in the LDCs would benefit by NOT enforcing restrictions on resale of these drugs (why not buy enough for your own medical uses and then buy some more to sell back in Amercia or Europe at high prices there?).  This question asks you to use basic game theory to analyze the strategic interaction between the multinational pharmaceutical companies (BigPharma) and the LDCs.

Suppose  Big Pharma has only two prices they can offer to LDCs, PH, price high , or PL, price low, and that LDCs have only two actions, ER, enforce restrictions on resale back to America/Europe, or not,  NER. Suppose payoffs can be described by 4 numbers: 0 which is a benchmark for the status quo, -1 (minus 1) which is a loss situation relative to the status quo, 1 which is better than the status quo, and 2 which is even better than 1. When Big Pharma charges a high price BigPharma and LDCs are indifferent about whether LDCs enforce restrictions or not, with a payoff of 0, for both players in both cases. When a low price is charged, BigPharma's payoff is 1 if LDC's enforce restrictions on resale and -1 if LDCs don't enforce restricitions on resale, while LDC's payoffs are 1 if LDC's enforce restrictions on resale and 2 if LDCs don't enforce restrictions on resale. [corrected from test paper]

4.1 Assuming Big Pharma moves first and the LDC's second; draw and label the game tree and use rollback reasoning to predict the strategies used by each player and the outcome of the game.

4.2 Assume Big Pharma and the LDC's play a simultaneous one-shot game. Draw and label the payoff matrix with BigPharma the row player and the LDCs the column player. Use game theory to predict the strategies used by each player and the outcome of the game (circle the startegies and payoffs clearly in your table).

4.3 Assuming the LDC's move first and Big Pharma second, draw and label the game tree and use rollback reasoning to predict the strategies used by each player and the outcome of the game. Briefly comment on the strategic similarities or differences with your answers in 4.1 and 4.2 .

Changing the order of the play changes the information structure of the game. When Big Pharma moves first, or simultaneously, with the LDCs it anticipates that the LDCs will act in their own best interests if Big Pharma prices low - ie by not enforcing the restrictions on resale, which is acting opportunistically from big Pharma's perspective. In the sequential game 4.1 LDCs can actually observe and respond afterwords to Big Pharma's prices by not enforcing restrictions on resale after Big Pharma has actually made the drugs available at a low price. In the simultaneous move game the LDCs can't observe and respond to the lower prices, but Big Pharma can anticipate that they will play their weakly dominant strategy of NER (it can never hurt and it might help the LDCs to always play NER in that game). SO in either of these first two games Big Pharma won't price Aids drugs low. Moving first is a disadvantage to them...and to LDCs. But if the LDCs move first,as in 3.2, they take away their ability to respond to Big Pharma after Big Pharma announces its prices - and this makes Big Pharma willing to offer lower prices becasue they only have to provide those low prices after observing that the LDCs have enforced restrictions against resale. The key idea here is that "moving first" for LDCs means committing to enforce restrictions on resale in such a way that big Pharma can directly observe that decision, confirm that it has happened, before they make their pricing decision. Removing their freedom to react and respond actually gives LDCs a better outcome......even though it ends up playing what looks like (in game 4.2) to be a dominated strategy...It wasn't sufficient to say "there is a first mover advantage" since moving first is good for one and bad for the other.....here.

Question 5 Muti Choice . There are 4 multi-choice questions here . Each question is worth 7 marks. Write your answer in your answer booklet.

Q5.a Consider the following two situations. (i) Two governments choose between two agricultural policies: Policy (A) simultaneously subsidizing their local farmers and taxing imported foods  and Policy (B) not imposing such tax/subsidy policies. Regardless of what other governments are doing, imposing A type policies  always increases the political payoff (in votes) earned by the politicians in the home country by 10 but also always decreases the payoff earned by the other country’s politicians by 5. (ii) Fans at a sporting event choose between cheering for the home team and not cheering. Regardless of what other fans are doing, cheering increases a fan’s enjoyment and thus always increases his or her payoff by 5, and also adds to the enjoyment of other fans and thus always increases their payoff by 1. Which of these situations has the characteristics of a prisoners’ dilemma?
(a) Only situation (i)
(b) Only situation (ii)
(c) Both situations (i) and (ii)
(d) Neither situation (i) nor situation (ii)
(e) there isn’t enough information to answer the question using Game theory

Q5.b Fishing Boat Owners (FBO) and the crews that work for them on the boats ( W) are playing an alternating offer bargaining game at the start of the fishing season. FBO and W must bargain together about how to share out the proceeds of the season's catch and they also have to work together to both catch the fish , which the crew does, and process it for sale, which the FBO’s do. The fishing season is short and lasts only 3 weeks, with the total value of the catch being $100 in week 1, $60 in week 2, and $40 in week 3, with no fishing permitted after that. Getting late to the fishing grounds means less fish to catch. Workers and FBO’s each have to be paid more than $10 to make it worth their while to work. Due to circumstances beyond anyone’s control the boat owners and workers can meet to make offers and ratify agreements only once a week. The bargaining rules are that the FBO’s make an offer of a division of the catch’s value in week 1. The workers either accept or reject. If they accept , they go off to fish in week 1 and the catch value is split as agreed. If the workers reject the FBO’s offer they have to wait until week 2 to make a counter offer to the FBO’s. At that time (week 2) the FBO’s can either accept the workers offer and have the (smaller value) catch harvested and share the money as agreed, or reject , wait until week 3 then come back with a counter-counter-offer to the workers. This last counter offer is either accepted , the catch harvested and the (smaller still) money shared out as agreed, or it is rejected , no fish are caught and they each walk away with nothing. Assume offers and counter offers are made in units of $1 (ie no fractions), that each player values only their net receipts (ie $share of the catch less the $10 cost of their work efforts) , and that either party has to be offered a strictly positive inducement to work over whatever the next best option at the time is. Choose the answer from the list below that is closest to the prediction that game theory would make about the outcome of this bargaining game, and write the answer in your answer booklet.

1. the owners will will hold out till week 3 and exploit the workers, dividing the $40 catch $29 for themselves and $11 for the worker, which the workers will grudgingly accept.
2. The FBO’s will keep 89 for themselves in the first week and offer the worker’s $1 more than the minimum $10 they will work for, and the workers will accept, grudgingly.
3. Same as above (2) except that workers reject this low offer and hold out till week 2 where they propose a $30, $30 split of the $60 proceeds , and the FBO’s will accept rather than run the risk of not getting an agreement before the season runs out.
4. The FBO’s will offer to split the first week catch evenly $50, $50 each and the workers will accept rather than delay and run the risk of get a lower share of a smaller pie later.
5. The FBO’s will offer a 2/3 and 1/3 split in week 1, with FBO taking $67 and the workers $33, the workers will accept rather than run the risk of having no contract later. (69 and 31 would be a more precise predicition but i didn't ask for this level of precision.....)

Q5.cThe following payoff matrix describes a 3 person simultaneous game. The three players are R, B, and G. Each player has two moves: {T, B} for R, {L, R} for B, and {Yes, No} for G. Payoffs are in dollars, listed in order from left to right first for player R, then for player B then for player G. The Nash Equilibrium prediction(s) for the outcome of this game is/are _____.d,h (Choose your answer(s) from the list a,b,c,d,e,f,g,h that labels each of the cells in the payoff matrixand enter it into your answer booklet)

d and h are both nash equilibria - find by best response method as per below -this is much like the 3 person prisoner's dilema game in the text.some of you - a few, but still some -are still not reading a payoff table propelry in order to be able to compare the relevant payoffs. Colouring in helps, but you're mixing up cpmparing columns and rows. If this appears to be a problem for you and you havent' figured out how to solve it please come and see me so we can get it straightened out.

Q5.d The table below represents a 2 player simultaneous game with payoffs in dollars indicated in standard fashion:The first two steps in a process of iterated elimination of dominated alternatives would first eliminate  strategy _____and second would eliminate strategy_____??(Choose an answer from the list of strategies T,L1,H,B,L2,M,R to fill in the blanks in this sentence, writing your answer in the form “first X then Y” or  write “no strategy can be eliminated” and enter your answer in your answer booklet)

Row H is dominated by Row T after which Coumn R can be eliminated .