Econ 223 Examination:  October 15 2010
3 hours max: 6:30 pm-9:30 pm

This is a closed book exam: no notes, no books, no cell-phones, no calculators  just  you. Your script will be taken from you and you will receive a zero grade for this paper  should you be found with any of these items – so please deposit them at the front of the room. On the desk space in front of you you should have

Before you leave the exam room tonight. Make sure your name and student ID are clearly written on the A4 answer sheet and place it inside your answer book. Please leave your answer book at your assigned desk space when you leave (to preserve alphabetic arranging of scripts). No one will be admitted after 7pm and you may leave any time after 7 pm

There are 12 multi choice questions 5 marks each, 60 in total.
There are 3 "written answer" type questions in Part B for a total of 40 marks.

A1 ( 5 marks) The game tree below represents a stylized 3 player (A, B, C) sequential game (no payoffs are shown at the terminal nodes).

How many strategies does player B have in this game?( ) 

A2 ( 5 marks) random breath checks The police have to decide whether to check for drinking drivers using roadblocks. Driver's have to decide whether to drink and drive or stay sober. Assume the game being played out by drivers and the police is a one shot simultaneous game with payoffs on a scale of 0 (bad) to 10 (very good) as show in the following 2x2 payoff matrix. You might not agree with these preferences - especially the preferences for the drivers - but assume for the sake of argument that drivers do want to drink and drive...and not get checked by the police, and that if they do stay sober they would prefer not to have the police stop and check them. The police on the other hand really do want to catch drinking drivers and they dislike not catching drinking drivers, while at the same time they would prefer not to waste resources checking sober drivers. There is a mixed strategy Nash equilibrium. In that mixed strategy Nash equilibrium the Drivers will be drinking and driving with what probability? On your multi choice answer sheet for A3 write down one of the integers 0,10%,20%,...through to ....90%,100% that is closest to your answer.

A3( 5 marks) 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. Assume Jack and Jill are both familiar with the strategic reasoning concepts from this course. Select from the following list the one idea from game theory that will most help them to improve their chances at getting the monetary prize.On your multi choice answer sheet write down the identifying letter for your answer).

 

A4 ( 5 marks) The 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 __b and 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)

A5 ( 5 marks) The following table describes a two-player game.

There are two cells in the payoff table where a payoff is unknown to us, but that payoff, indicated by the same value Z in both cases, will equal one of the numbers 3, 6, 10. Suppose that Row Player is able to make a strategic move to commit herself to either action T or action B before Column Player moves. Row Player ‘s commitment is observable by Column player and irreversible, and she is confident that Column Player will react in a rational manner according to the payoffs expressed in the table. The payoff Z can take on one of three possible values 3, 6, 10. Complete the following sentence:In this situation, Row Player would choose to commit to action T if Z = __3 or 6 ___. Choose an answer - or answers - from the list {3, 6, 10, None, All } and enter it in your answer book)

A6 ( 5 marks) Ski field companies like to employ pleasant mannered people . It is difficult, if not impossible, for the employing agency to directly observe skills at being pleasant mannered . So they ask potential employees to participate in a series of time consuming workshops on being a ski lift operator where potential employeeswill be assessed on their demonstrated abilities to be pleasant under a variety of stressful conditions. The employers make a salary offer of $10,000 for a season's work as a lift oprator those who successfully complete n workshops, and an offer of $7900 for a job doing maintenance work on the ski field for those who don't complete the n workshops.

Lets suppose that there are only two types of applicants, those who have the required skills, the "haves" (H), and those who don't, the "have nots" (HN). Each applicant knows what type they are. Doing a course is hard work, but a little easier for the Haves than the Have Nots. The time and effort costs for a Have to successfully complete a course is $500 per course (assessed by the applicant themselves as a "money equivalent" for the time and effort per workshop). The time and effort costs for a Have Not to successfully complete a course is twice as much, $1000 per course. What is the smallest and what is the largest number n of courses that will satisfy the incentive compatability constraints for this problem of asymmetric information? Select your answer from the following list and write your selection(s) on your multi choice answer sheet. Note this question asks you to write down two responses unless you choose (a).

10000-500*n > 7900 is required for the HAves to want to take the course (so the highest n can be is n=4

10000-1000*n < 7900 is required for the HAve Nots to NOT want to take the course (so the lowest n can be is n=3

 

A7 ( 5 marks) Game theory argues that cooperative behaviour and mutually beneficial outcomes can be sustained in a repeated 2 player prisoner's dilemma game when players use tit-for-tat  (TFT) or grim (G) strategies in an indefinitely repeated game. These two trigger strategies have some (but not all) features in common when played in a Nash equilibrium that sustains cooperation. Select which features the grim strategy has. : (Choose your answer(s) from below and enter it on your multi-choice answer sheet - there may be more than one correct answer, marks are awarded only for a complete set of correct answers) red marks the answers

 

A8  ( 5 marks) Consider the following two situations. (i) Two governments choose between imposing (cleverly designed) restrictions on international trade and not imposing such restrictions. Regardless of what other governments are doing, imposing such restrictions always increases the payoff earned by the home country by 5 but also always decreases the payoff earned by the other country by 10. (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 3, but it frustrates fans of the other team , reducing their payoff by 6. Which of these situations has the characteristics of a prisoners’ dilemma? (Choose an answer from the list below and enter it on your multi-choice answer sheet):

A9   ( 5 marks) Consider a variant of chicken in which each driver can go straight, swerve to his left, or swerve to his right. If one swerves to his left and the other swerves to his (own) right, then the cars will collide, just as they will if both drivers go straight. The payoff table is as immediately below. Write the all the letters of the cells that correspond to the Nash Equilibria of this game

 

Part B 3 Questions (55 marks)

 

Question B1 2x2 Games (20 marks) This question is on the reverse side of your multi-choice answer sheet . Answer questions in the spaces provided on that sheet.

Question B2: inverse probability (10 marks) (write answers in answer book)

Part B2.1 (5 marks):Some young adults (ages 18-25) use soft drugs (SD) like marijuana, some consume hard drugs (HD) like heroin and P, and some use both. Older adults (especially some politicians) argue that SD use leads to HD use, not for sure, but with a pretty high - ie 90% - chance. These people base their beliefs on a survey that a large proportion of hard drug users, 90%, have used soft drugs. You investigate this claim by going back to the detail of the survey: of the 1000 young adults surveyed only 40 actually used hard drugs. In the survey 90% of those (36) used soft drugs as well and th eother 4 didn't. You also note that of the other 960 in the survey who did not use hard drugs, 324 of them used soft drugs and 636 of them did not use either soft or hard drugs. Based on your investigations and your knowledge of inverse probability reasoning make a probability assessment of the chances that a young adult (ages 18-25) who uses soft drugs will also use hard drugs. Briefly explain your answer. (fractions OK, no need to reduce them to decimals...)

Part B2.2 (5 marks): Employee turnover in the service industries is a problem in in New Zealand. About 10 out of 100 employees who have been employed for one year will leave their job the next year (call them EQ="early quitters" . Employers don't like to hire people who are going to quit shortly after their first year on the job. A consultant hired by the employer believes that it is potentially fertile young women (aged 20-35) that are the "problem". However sexist this seems, she ( a middle aged female consultant) backs up their argument with statistics showing that of those early quitters 60% are young women, while for those that stay on after that first year only 50% are young women. So, argues the consultant, young females are significantly "over represented" in the population of "early quitters" and they have a 60% chance of quitting after their first year. Do you agree with this assessment or not? How would you, as an intelligent rational player of games, using the same statistics as the conslutant, advise employers about the chances of a female being a "quitting" type? Briefly explain your answer. (fractions OK, no need to reduce them to decimals...)

 

B3 Strategic moves (25 marks) (write answers in answer book)

Consider the following stylized game between parents and their university age teenager in her last year of college. The teenager (player T) moves first, either working hard on their Uni degree and graduating (G) or dropping out D and spending lots of time on the ski fields. Parents (player P) observe what the teenager has done at the end of year and either provide a reward (R) in the form of an overseas trip (Nz to Europe for 3 months) or give no reward but simply praise their daughter with words. Preference ranks (higher numbers more preferred) for both players are given as in the follwoing game tree, and for the parent reflect the fact that giving this reward is very costly, so they'd prefer not to if they don't have to.

1) (5 marks) Analyze this sequential game using game theory , then represent it as a simultaneous game, identify all Nash Equilibria, and all subgame perfect equilibria.

2) (20 marks) The parents wish to make a strategic move to change the outcome of this game , explicitly promising that they will provide a reward if their daughter graduates . Explain the credibility problem involved in using this strategic promise to try to change the outcome of the game. Then identify and briefly explain (in one or two sentences) all the methods for solving credibility problems for strategic moves that Dixit and Skeath identify in Chapter 10 , briefly explaining which ones might be relevant to solving the credibility problem here.