Econ 223 TEST Friday June 9 2006

You have up to three hours to complete this exam. The start time is 6:00, the finish time is 9:00. You may turn in your exam paper and leave the examination room (quietly please) any time after 7pm.

You should have two items with your name and student ID on: a hand written answer booklet and a multi choice answer sheet. Be sure to sign the multi-choice answer sheet and exam booklet and check that your name and student ID are printed correctly on both your multi-choice answer sheet and on your written-answer booklet. Answer sheets without signed names will not be marked.  WHEN YOU LEAVE SIMPLY LEAVE YOUR BLUE ANSWER BOOKLET (with multi-choice answer sheet inside) ON THE DESKTOP IN FRONT OF YOU - I will collect the exams in alphabetical order when the test is finished.

A Multi Choice Questions  (9 questions, 5 marks each)

On your multi-choice your answer sheet for part A clearly indicate your response by circling your answer , as in the following example

A 1 : The following table describes a two-player simultaneous game. There is one payoff that is unknown to us, but that payoff (Z) will equal 3, 6, or 9.


Complete the following. In this game, there are no pure strategy Nash equilibrium but there is a mixed strategy equilibrium when Z is = _____. (Choose an answer from the list below to fill in the blank and enter it on your multi-choice answer sheet)
(a)            9 only
(b)            6 only
(c)            3 only
(d)           either 3 or 6
(e)           either 6 or 9
(f)            either 3 or 9
(g)           either 3, 6 or 9
(h)           none of the above : the level of Z is irrelevant in this game

A 2          Consider the following two situations. (i) The airport managers of two city governments, Auckland and Christchurch, choose simultaneously and independently between giving special concessions to large international airlines to fly direct into their local airports and not giving such concessions. Regardless of what the other city does , giving such concessions increases the payoffs (votes, tourist income) of the city giving the concessions by 5, but also decreases the payoff earned by the other city by 10. (ii) Fans at a rugby game between Auckland and Christchurch choose between cheering for their preferred team and not cheering. Fans are looking to have a good time, rated on a scale from 1 (worst) to 10 (best) , but rugby games can be loud and noisy. Regardless of what fans for the other team are doing , cheering for your preferred team increases a fanÕs payoff by 3 preference ranks , but it reduces the payoff of fans who like the other team team by 1 preference rank. Which of these situations has the characteristics of a prisonersÕ dilemma? (Choose an answer from the list below and enter it on your multi-choice answer sheet):

A 3    Some young adults in modern urban communities use soft drugs (SD) like marijuana, some consume hard drugs (HD) like heroin and P, and some use both. A politician argues that SD use leads to HD use, not for sure, but with a pretty high chance. She bases her beliefs on a survey that showed 4 out of 5 hard drug users, ie 80%, have used soft drugs.You investigate this inference by going back to the detail of the survey: of the 100 young adults surveyed only 5 out of 100 (5%) actually used hard drugs , and it is true that 4 of those 5 used soft drugs as well. But you also find in the survey results that of the other 95 who did not use hard drugs, 60 of them used soft drugs and 35 used no drugs at all. Based on your investigations and your knowledge of inverse probability and Bayes theorem you would make a rough assessment that the probability of a young adult using hard drugs given that soft drugs are being used,P(HD|SD), is: (Choose an answer from the list below and enter it on your multi-choice answer sheet)

A 4    Farmers (F) and SmithÕs City (SC) both sell household appliances such as dishwashers, refrigerators, stoves, etc. They tend to carry the same brands so the major dimension they compete on is price. Suppose each store has only two pricing policies, High (H) or Low (L), and that each firm chooses their pricing policies monthly, simultaneously and independently. Each firm can observe what prices the other firm charges in previous months. Payoffs are such that each stage game is a prisoner's dilemma, with a large temptation to "cheat" on any cooperative, high price outcome, and a low payoff for being a "sucker". Suppose that this game is repeated month after month, more or less indefinitely into the future. Each firm has hired a game theorist as a consultant. The consultants explain that the Commerce Commission in NZ will prosecute firms for communicating with each other and coming to an explicit agreement to keep prices high. But they do suggest that a better result could occur if the playerÕs used tit-for-tat  (TFT) or the grim (G) strategy in this repeated game. Which of the following observations is most likely to be correct in this particular situation on the basis of game theory? (Choose an answer from below and enter it on your multi-choice answer sheet) 

A 5  The game tree below represents a stylised 3 player (A, B, C) sequential game (no payoffs are shown at the terminal nodes).

How many strategies does player C have in this game?(Choose an answer from below and enter it on your multi-choice answer sheet) 

A 6      An insurance company is thinking about introducing two broad types of automobile insurance for international tourists visiting the country. One policy A has a high excess ($1000) and a low monthly premium ($100 per month) , the other policy B has a low excess ($200) and a higher premium ($300 per month). Their current policy C, which they will stop offering if they decide on the 2-tier policies A and B, is a moderate excess ($500) and a medium premium ($200 per month). The managers of the company think that there are basically two types of visiting customers who will buy auto insurance from them, high risk drivers who are more likely to have accidents, and low-risk drivers who are less likely to have accidents. They are wondering whether it would be more profitable to separate out the market by offering differing policies for different types. You have just been hired as a consultant and you make the observation that customers might know whether they are high or low risk but the company doesn't know this. Moreover, because the tourists come from a wide range of overseas countries, it will be difficult, if not impossible, to find reliable information on previous accident records. You point out that what the managers are effectively trying to do with the high and low excess policies A and B is set up a screening device. Whether and how it will work depends on a combination of two critical factors: the proportion of high and low risk types in the population of visiting tourists and the size of the difference in accident risk probabilities for each of the two types. Each square in the following table represents a combination of those two critical factors.

Complete the following. The separating equilibrium in which high risk types voluntarily choose the low excess policy and low risk types voluntarily choose the high excess policy is associated with which cell(s) in the graph _____. (Choose an answer from below to fill in the blank and enter it on your multi-choice answer sheet) 

A 7 Column player has three pure strategies A,B and C and Row player has strategies T,M and B with payoffs in terms of preference ranks as indicated in the payoff matrix below (higher numbers indicate more preferred alternatives)

In the mixed strategy Nash equilibrium of this game the Row player will:(Choose an answer from the list below and enter it on your multi-choice answer sheet)

A 8      Before the Allied invasion of France in 1944, the Germans had to decide where to place their defenses. They had three choices: they could concentrate their defenses at Calais (GC), concentrate at Normandy (GN), or split their defenses between both locations (GS). The Allies had two choices: they could attack at Calais (AC) or at Normandy (AN). Assume that this is a zero-sum game and that the possible outcomes are ranked as in the following matrix (where larger positive numbers represent outcomes more favorable for the Allies).

Assume that this game is played sequentially, with the Germans' having the first move. In the rollback equilibrium outcome of this sequential game, (Choose an answer from the list below and enter it on your multi-choice answer sheet)

A 9    Robert Gibbons described the situation of two firms that produce products that consumers may use together (for instance, a computer and software). The most important concern for these two firms is that they coordinate their product designs and agree on one set of technical standards (either both pick standard A or both pick standard B) that will make their products compatible with each other. Such coordination will leave both firms much better off than they would be with no coordination. As a secondary concern, each firm has its own favorite standard that it would most like to see both firms adopt. The game between these two firms (in which each chooses its standard simultaneously and independently ) can be best described by saying that is it most like a : (Choose an answer from the list below and enter it on your multi-choice answer sheet)
(a) a prisonersÕ dilemma game.
(b) a chicken game.
(c) a battle of the sexes game.
(d) an assurance game.
(e) a game with no Nash equilibrium in pure strategies
(f) an entry deterrence game
(g) a voluntary contributions (VCM) game
(h) a centipede game
(i) an ultimatum game

 

Part B Simultaneous games Multiple Choice. (10 questions 3 marks each, 30 marks in total )

The 10 payoff matrices on your multi choice answer sheet for part B describe various types of 2 player simultaneous games. Payoffs to players are the numbers 1,2,3,4 indicating preference rank. Higher numbers indicate better outcomes, so for example  4=best & 1=worst. On the answer sheet provided (1) write in the answer box for each question the option, or set of options, from the following list ("a" through "h") that most accurately describes the game AND (2) identify all pure strategy equilibrium strategies for each game (in some cases more than one option from the list may be appropriate). You do NOT have to rewrite the payoff matrix in your hand-written answer booklet. Write your answer on your multi-choice answer sheet. To identify the equilibrium cells clearly CIRCLE the relevant cell. Here is an example of how to fill in your answer sheet:

template

 Question C 25 marks

Answer this question in handwriting in your answer booklet.

Parent child relationships are complex. But lets examine a simplified version of one small piece of a one-shot interaction between a parent and child about schoolwork. The parent can either reward (R) or not (NR) a child for working hard (WH) , and either punish (P) or not punish (NP) the child for being lazy (L) . The following diagram illustrates this sequential 2x2 game. Payoffs are in preference ranks (4= best, 1=worst) using standard notation. Note that the parent wants the child to work hard rather than be lazy, but the parent's payoffs are such that rewarding is costly to the parent - eg the parent might have to spend a large amount of money on a reward (eg a bicycle or a ski trip) if the child works hard, so would rather not reward in this circumstance. Punishments on the other hand aren't so costly for the parent as they can be implemented by, for example, taking away privileges (playing video games, watching TV) from the child, and anyway, this parent prefers to punish a lazy child.

c1 (7 marks) Find the rollback equilibria of this game, then analyze this sequential game as a simultaneous game to identify all pure strategy nash equilibria as either sub game perfect (SPE) or not.

c2 (18 marks) The parent would like to make a strategic move to change the game by promising to reward the child for working hard. Explain the credibility problems the parent faces and how she might solve them? (A good answer will briefly identify all the methods Dixit and Skeath describe and check which might be strategically relevant and/or useful for the parent in this situation).

End